## n-CARDMATH Publications

- B. Sankara Gomathi, L. Ganesan and S. Arumugam, Architecture proposed for new method of partitioning high speed fractional image compression, Journal of Engineering and Applied Sciences 2(3)(2007), 558-563.
- S. Arumugam and I. Sahul Hamid, Simple Acyclic Graphoidal covers in a graph, Australasian Journal of Combinatorics, 37(2007), 243-255.
- R.N. Ashlin Deepa , R. Subramanian, S. Arumugam, Recognition of Handwritten Characters through Multiset of Puzzle Pieces, Proceedings of the Third National Conference on Advanced Image processing and Networking, National Engineering College, Kovilpatti, 2007, 595-603.
- S. Arumugam and I. Sahul Hamid, Graphs with unique minimum simple graphoidal cover, Indian Journal of Mathematics 49(2)(2007), 151-163.
- R.M. Suresh and S. Arumugam, Fuzzy technique based recognition of handwritten characters, Image and Vision Comput., 25(2) (2007), 230-239.
- S. Arumugam and M. Subramanian, Edge Subdivision and Independence Saturation In A Graph, Graph Theory Notes of New York, LII (2007), 9-12.
- B. Sankaragomathi, L. Ganesan and S. Arumugam, Fractal Image Compression Applied to Remote Sensing, Proc. XXI. Internatinal Conference on Computer, Electrical and System Science and Engineering, 2007 (CESSE 2007), 386-391.
- S. Arumugam, K. Jacob and Lutz Volkmann, Total and Connected domination in digraphs, Australasian Journal of Combinatorics, 39(2007), 283-292.
- S. Arumugam and K. Rejikumar, Fractional Independence and Fractional Domination Chain in Graphs, AKCE. J. Graphs. Combin., 4(2)(2007), 161-169.
- S. Arumugam and M. Subramanian, Independence Saturation and Extended Domination Chain in Graphs, AKCE. J. Graphs. Combin., 4(2)(2007), 171-181.
- B.D. Acharya, S. Arumugam and P.J. Slater, Domination in Discrete Structures - New Directions, AKCE. J. Graphs. Combin., 4(2)(2007),113-115
- H. B. Walikar, B. D. Acharya, H. S. Ramane H. G. Shekharappa and S. Arumugam, Partially Balanced Incomplete Block Designs Arising From Minimal Dominating sets of a Graph, AKCE. J. Graphs. Combin., 4(2)(2007), 223-232.
- B. Sankaragomathi, L. Ganesan, S. Arumugam, Encoding Video Sequences in Fractional-Based Compression, Fractals, 15(4)(2007), 365-378.
- B. Sankara Gomathi, L. Ganesan and S. Arumugam, A practical approach to colour imaging compression using partitioned iterated function system, Advances in Modelling and Analysis B: Signals, Information, Patterns Data Acquisition, Transmision Processing and Classification, 50(1,2) (2007) 1-17.
- K.G Srinivasagan, L. Ganesan and S. Arumugam, Tamil Handwritten Word Recognizer, Advances in Modelling and Analysis B: Signals, Information, Patterns Data Acquisition, Transmision Processing and Classification,50(1,2) (2007), 64-77.
- K.G Srinivasagan, L. Ganesan and S. Arumugam, Hidden Markov Model based Tamil Handwritten Character Recognition, Advances in Modelling and Analysis B: Signals, Information, Patterns Data Acquisition, Transmision Processing and Classification,50(3,4) (2007), 1-14.
- B. D. Acharya and S. Arumugam, Labelings of Discrete Structures – New Challenges, Labelings of Discrete Structures and Applications, Ed B. D. Acharya, S. Arumugam and A. Rosa. Narosa Publishing House, (2008), 1-14.
- B. D. Acharya, S. B. Rao and S. Arumugam Embeddings and NP-Complete problems for Graceful Graphs, Labelings of Discrete Structures and Applications, Ed. B. D. Acharya, S. Arumugam and A. Rosa, Narosa Publishing House, (2008), 57-62.
- S. Arumugam, A Note On Graceful Labelings and Graph Decomposition, Labelings of Discrete Structures and Applications, Ed. B. D. Acharya, S. Arumugam and A. Rosa, Narosa Publishing House, (2008), 63-68.
- S. Arumugam and S. Meena, Common Weight Decomposition Into Minimum Acyclic Graphoidal Covers, Labelings of Discrete Structures and Applications, Ed. B. D. Acharya, S. Arumugam and A. Rosa, Narosa Publishing House, (2008), 69-76.
- S. Arumugam and I. Sahul Hamid, Label Graphoidal Covering Number of a Graph, Labelings of Discrete Structures and Applications, Ed. B. D. Acharya, S. Arumugam and A. Rosa, Narosa Publishing House, (2008), 77-82.
- S. Arumugam and I. Sahul Hamid, Simple Graphoidal Covers in a Graph, J. Combin. Math. Combin. Comput., 64(2008), 79-95.
- S. Arumugam and Sithara Jerry, A note on independent domination in graphs, Bulletin of the Allahabad Mathematical Society, 23(1) (2008), 57-64.
- S. Arumugam, I. Sahul Hamid, Simple path covers in Graphs, International J. Math. Combin., 3(2008), 94-104.
- S. Arumugam, I. Sahul Hamid and A. Muthukamatchi, Independent Domination and Graph Colorings, Proc. of ICDM 2006, Ramanujan Mathematical Society Lecture Notes Series No. 7, 2008, 195-203.
- S. Arumugam and K. Reji Kumar, Basic Minimal Dominating Functions, Utilitas Math., 77 (2008), 235-247.
- B. Sankaragomathi, L. Ganesan and S. Arumugam, Performance of applying Fractal Coding on audio data, Int. J. Singnal and Imaging Systems Engineering, 1(3/4) (2008), 238-244
- S. Arumugam and J. Suresh Kumar, Tree t-spanners of a graph, J. of Combinatorics, Information and System Sciences, 33(3-4) (2008), 163-169.
- K. Reji Kumar, S. Arumugam and Gary MacGillivray, On Maximal Fractional Independent Sets In Graphs, Ars Combinatoria, 87(2008), 205-212.
- S. Arumugam and C. Sivagnanam, Neighborhood connected and neighborhood total domination in graphs. Proc. Int. Conf. on Disc. Math., (2008), 45-51.
- S. Arumugam, Coloring and Domination in Graphs, The Mathematics Student, 77(1-4)(2008), 119-129.
- S. Arumugam, K.A. Germina and V. Ajitha, On (k,d) multiplicative indexable graphs, J. Combin.Math. Combin. Comput., 69(2009), 15-21.
- S. Arumugam, T.M.K. Anandavally, K.A. Germina and S.B. Rao, On sum composite graphs and embedding problems, J. Combin.Math. Combin. Comput., 69(2009), 23-30.
- S. Arumugam and Hebzibai Jeyakumar, Asteroidal Chromatic Number of a Graph, J. Combin.Math. Combin. Comput., 69(2009), 39-44.
- S. Arumugam and I. Sahul Hamid, Graphs with unique minimum simple acyclic graphoidal cover, J. Combin.Math. Combin. Comput., 69(2009), 45-52.
- V. Ajitha, S. Arumugam and K.A. Germina, On square sum graphs, AKCE. J. Graphs. Combin., 6(1) (2009), 1-10.
- S. Arumugam, G.S. Bloom, Mirka Miller and Joe Ryan, Some Open Problems on Graph Labelings, AKCE. J. Graphs. Combin., 6(1) (2009), 229-236.
- S. Arumugam, S. Velammal, Connected Edge domination in graphs, Bulletin of Allahabad mathematical Society, 24(1) (2009), 43-49.
- S. Arumugam and Sithara Jerry, Fractional Edge Domination in Graphs, Appl. Anal. Discrete Math.3(2009), 359-370.
- S. Arumugam and R. Kala, A Note on Global Domination in Graphs, Ars Combinatoria, 93(2009), 175-180
- A. Anitha, S. Arumugam and E. Sampathkumar, Degree Equitable Sets in a Graph, International J.Math. Combin., 3(2009), 32-47.
- S. Arumugam, K.A. Germina and T.M. K. Anandavally, On Additively Geometric Graphs, J. Combin. Math. Combin.Comput., 70 (2009), 207-216.
- S. Arumugam, O. Favaron and S. Sudha, Irredundance Saturation Number of a Graph, Australasian Journal of Combinatorics, 46(2010), 37-49.
- S. Arumugam, K. Karuppasamy and I. Sahul Hamid, Fractional Global Domination in Graphs, Discussiones Mathematicae Graph Theory, 30(2010), 33-44.
- S. Arumugam and S. Sudha, Min-Max Dom-Saturation Number of a Tree, International J.Math. Combin., 2(2010), 45-52.
- A. P. Santhakumaran, S. Arumugam, Radius and Diameter with Respect to Cliques in Graphs, J. Combin. Matha.Combin.Comput., 72(2010), 231-241.
- S. Arumugam and C. Sivagnanam, Neighborhood Connected Domination in Graphs, J. Combin.Math. Combin. Comput., 73(2010), 55-64.
- S. Arumugam and Sithara Jerry, The convexity graph of minimal dominating functions of a graph, Proc. Jangjeon Math. Soc., 13 (2)(2010), 219-230.
- S. Arumugam and M. Sundarakannan, On k-Equivalence Dominating Sets in Graphs, International J.Math. Combin., 4 (2010), 86-93.
- L. Benedict Michaelraj, S.K. Ayyaswamy and S. Arumugam, Chromatic Transversal Domination in Graphs, J. Combin. Math. Combin. Comput., 75(2010), 33-40.
- A. Anitha, S. Arumugam, S.B. Rao and E. Sampathkumar, Degree Equitable Chromatic Number of a Graph, J. Combin. Math. Combin. Comput., 75(2010), 187-199.
- S. Arumugam and C. Sivagnanam, Neighborhood Connected Domatic Number of a Graph, J. Combin. Math. Combin. Comput., 75(2010), 239-249.
- S. Arumugam, K. Raja Chandrasekar and S. Sudha, Irredundant and Open Irredundant Colorings of Graphs, Bulletin of the Institute of Combinatorics and Applications, 61(2011), 24-36.
- S. Arumugam, Teresa W. Haynes, Michael A. Henning and Yared Nigussie, Maximal Independent Sets in Minimum Colorings, Discrete Math., 311(2011), 1158-1163.
- S. Arumugam, Domination in Graphs, Graph Theory Research Directions, Eds. Pratima Panigrahi and S.B. Rao, Narosa Publishing House, (2011),35-47.
- S. Arumugam and C. Sivagnanam, Neighborhood Total Domination in Graphs, Opuscula Mathematica, 31(4) (2011), 519-531.
- A. Anitha, S. Arumugam and Mustapha Chellali, Equitable Domination in Graphs, Discrete Mathematics, Algorithms and Applications, 3(3)(2011), 311-321.
- S. Arumugam and Latha Martin, Degrees and Degree Sequence of k-edge d-critical graphs, Journal of Discrete Mathematical Sciences & Cryptography, 14(5) (2011), 421-429.
- S. Arumugam, K. Raja Chandrasekar, Neeldhara Misra, Geevarghese Philip and Saket Saurabh, Algorithmic Aspects of Dominator Colorings in Graphs, In IWOCA 2011, C.S. Iliopoulos and W.F. Smyth (Eds.), Springer-Verlag, Lecture Notes in Comput. Sci., 7056 (2011), 19-30.
- S. Arumugam and B. Vasanthi, Graph Theoretic Models for Social Networks- A Brief Survey, The Mathematics Student, 80 (1-4) (2011), 209-229.
- S. Arumugam and Jay Bagga, Graceful Labeling Algorithms and Complexity -A Survey, J. Indones. Math. Soc., Special Edition (2011), 1-9.
- S. Arumugam, Dalibor Froncek and N. Kamatchi, Distance Magic Graphs-A Survey, J. Indones. Math. Soc., Special Edition (2011), 11-26.
- S. Arumugam, Metric Dimension in Graphs-A Brief Survey, Mathematical and Computational Models, Eds. R. Nadarajan, R.S. Lekshmi and G. Sai Sundara Krishnan, Narosa Publishing House, New Delhi, (2012), 318-325.
- S. Arumugam and K. Raja Chandrasekar, Minimal dominating sets in maximum domatic partitions, Australasian Journal of Combinatorics, 52 (2012), 281-292.
- S. Arumugam and Varughese Mathew, The Fractional Metric Dimension of Graphs, Discrete Math., 312(9) (2012), 1584-1590.
- S. Arumugam and M. Nalliah, Super (a,d)-edge antimagic total labelings of friendship graphs, Australasian Journal of Combinatorics, 53 (2012), 237-243.
- S. Arumugam, Varughese Mathew and K. Karuppasamy, Fractional Distance Domination in Graphs, Discussiones Mathematicae Graph Theory , 32 (2012), 449-459.
- S. Arumugam and M. Sundarakannan, The equivalence chain of a graph, J. Combin. Math. Combin. Comput., 80 (2012), 277-288.
- S. Arumugam and M. Sundarakannan, Equivalence domination number of a tree, Proc. Jangjeon Math. Soc., 15(3) (2012), 317-323.
- S. Arumugam and K. Raja Chandrasekar, A note on graphs with open irratic number two, Bulletin of ICA, 65 (2012), 27-32.
- S. Arumugam and N. Kamatchi, On (a, d)-distance antimagic graphs, Australasian Journal of Combinatorics, 54 (2012), 279-287.
- S. Arumugam, Jay Bagga and K. Raja Chandrasekar, On Dominator Colorings in Graphs, Proceedings Mathematical Sciences, 122(4) (2012), 561-571.
- S. Arumugam and K. Raja Chandrasekar, On Chromatic Transversal Domination in Graphs, J. Combin. Math. Combin. Comput.,83 (2012), 13-21.
- S. Arumugam and Sithara Jerry, The Convexity Graph of Minimal Total Dominating Functions of a Graph, Kragujevac J. Math. 36 (1) (2012), 119-131.
- R. Anantha Kumar and S. Arumugam, Pairwise distance similar sets in graphs, J. Combin. Math. Combin. Comput., 84 (2013), 21-28.
- N. Kamatchi and S. Arumugam, Distance antimagic graphs, J. Combin. Math. Combin. Comput., 84 (2013), 61-67.
- R. Lakshmanan, S. Arumugam and Atulya K. Nagar, Visual cryptography scheme for the mindom access structure of a graph, J. Combin. Math. Combin. Comput., 84 (2013), 69-80.
- M. Nalliah and S. Arumugam, Super (a,d)-edge-antimagic total labelings of generalized friendship graphs, J. Combin. Math. Combin. Comput., 84 (2013), 81-90.
- S. Arumugam, R. Lakshmanan, and Atulya K. Nagar, Graph Access Structures With Optimal Pixel Expansion Three, Information and Computation, 230 (2013), 67-75.
- S. Arumugam, Mustapha Chellali, and Teresa W. Haynes, Equivalence Domination in Graphs, Quaestiones Mathematicae, 36 (2013), 331-340.
- S. Arumugam and M. Sundarakannan, Equivalence Dominating Sets in Graphs, Utilitas Mathematica, 91 (2013), 231-242.
- S. Arumugam, Karam ebadi and L. Sathikala, Twin Domination and Twin Irredundance in Digraphs, Applicable Analysis and Discrete Mathematics, 7 (2013), 275-284.
- S. Arumugam, R. Lakshmanan and Atulya K. Nagar, Visual cryptography scheme for graphs with vertex covering number two, Natl. Acad. Sci. Lett., 36(6) (2013), 575-579.
- S. Arumugam, Varughese Mathew and Jian Shen, On Fractional Metric Dimension of Graphs, Discrete Mathematics, Algorithms and Applications, 5 (4) (2013), 1350037 (8 pages)
- S. Arumugam, Bibin K. Jose, Csilla Bujtas and Zsolt Tuza, Equality of Domination and Transversal Numbers in Hypergraphs, Discrete Applied Mathematics, 161 (2013), 1859-1867.
- S. Arumugam, Martin Baca, Dalibor Froncek, Joe Ryan, Kiki A. Sugeng, Some open problems on graph labelings, AKCE Int. J. Graphs Comb., 10(2) (2013), 237-243.
- S. Arumugam, I. Sahul Hamid and V.M. Abraham, Decomposition of Graphs into Paths and Cycles, Journal of Discrete Mathematics, vol. 2013, Article ID 721051, 6 pages, 2013. doi:10.1155/2013/721051.
- S. Arumugam and M. Sundarakannan, On Equality in an Upper Bound for the Equivalence domination Number, Quaestiones Mathematicae, 37 (2014), 1-9.
- S. Arumugam, Mirka Miller, Oudone Phanalasy and Joe Ryan, Antimagic Labeling of Generalized Pyramid Graphs, Acta Mathematica Sinica, English Series, 30(2) (2014), 283-290.
- S. Arumugam, D. Haughton, B. Vasanthi, C. Zhang, Reciprocity in social networks - A case study in Tamil Nadu, India, CS-BIGS, 5(2) (2014), 126-131.
- S. Arumugam, N. Kamatchi and G.R. Vijayakumar, On the uniqueness of D-vertex magic constant, Discussiones Mathematicae Graph Theory, 34 (2014), 279-286.
- Neil Buckley, Atulya K. Nagar and S. Arumugam, Key-Based Steganographic Textual Secret Sharing for Confidential Messaging, In M. Pant et. Al (eds.) Proceedings of the Third Interantional Conference on Soft Computing for Problem Solving, Advances in Intelligent Systems and Computing, Springer 258 (2014), 25-34.
- Neil Buckley, Atulya K. Nagar and S. Arumugam, AnimVSS: Frame-Based Visual Secret Sharing, In M. Pant et. Al (eds.) Proceedings of the Third Interantional Conference on Soft Computing for Problem Solving, Advances in Intelligent Systems and Computing, Springer 258 (2014), 35-44.
- S. Arumugam, R. Lakshmanan and Atulya K. Nagar, On (k,n)*-Visual Cryptography Scheme, Des. Codes Cryptogr., 71 (1) (2014), 153-162.
- S. Arumugam, Karam Ebadi and Martin Manrique, Co-Secure and Secure Domination in Graphs, Util. Math., 94 (2014), 167-182.
- Neil Buckley, Atulya K. Nagar and S. Arumugam, Visual Secret Sharing between Remote Participants, International Journal of Computer Applications, 103(2) (2014), 8-17. 2015
- S. Arumugam, D. Haughtom, B. Vasanthi and C. Zhang, A comparative study of reciprocity in two rural social networks in Tamil Nadu, India. CS-BIGS, 6(1) (2015), 37-46.
- S. Arumugam and M. Sundarakannan, On Equality in an Upper Bound for the Equivalence domination Number, Quaestiones Mathematicae, 38(1) (2015), 63-71.
- Martin Manrique and S. Arumugam, Vertex and Edge Dimension of Hypergraphs, Graphs and Combinatorics, 31(2015), 183-200.
- S. Arumugam, Karam Ebadi and Martin Manrique, Co-Roman Domination in Graphs, Proceedings Mathematical Sciences, 125(1) (2015), 1-10.
- J. Bagga, L. Pauline Fotso, P. Biatch Max and S. Arumugam, New Classes of Graceful Unicyclic Graphs, Electronic Notes in Discrete Mathematics, 48 (2015), 27-32.
- M. Balakrishnan, G. Marimuthu and S. Arumugam, Vertex In-magic Arc Labelings of Digraphs, Electronic Notes in Discrete Mathematics, 48 (2015), 33-39.
- Jessica Pereira, T. Singh and S. Arumugam, On (k,d)-Skolem Graceful Graphs, Electronic Notes in Discrete Mathematics, 48 (2015), 81-88.
- S. Arumugam and M. Nalliah, Super (a,d)-Edge antimagic total labeling of Friendship and generalized Friendship Graphs, Electronic Notes in Discrete Mathematics, 48 (2015), 103-110.
- S. Arumugam, M. Balakrishnan and G. Marimuthu, E-Super vertex In-magic total labeling of Digraphs, Electronic Notes in Discrete Mathematics, 48 (2015), 111-118
- N. Kamatchi, A. Ramalakshmi, S. Nilavarasi and S. Arumugam, A note on Distance Magic and Distance antimagic graphs, Electronic Notes in Discrete Mathematics, 48 (2015), 183-187.
- A. Godingo, T. Singh and S. Arumugam, On S-magic Graphs, Electronic Notes in Discrete Mathematics, 48 (2015), 267-273.
- Jessica Pereira, T. Singh and S. Arumugam, A new measure for gracefulness of graphs, Electronic Notes in Discrete Mathematics, 48 (2015), 275-280.
- B. Vasanthi, S. Arumugam, Atulya K. Nagar and Sovan Mitra, Applications of Signed Graphs to Portfolio Turnover Analysis, Proceedia-Social and Behavioral Sciences, 211(2015), 1203-1209.
- P. Jeya Bala Chitra and S. Arumugam, Resolving Sets without Isolated vertices, Procedia Computer Science 74 ( 2015 ), 38-42
- S. Arumugam, B. Jayaram and K. Thulasiraman, Independent Dominator Sequence Number of a Graph, Procedia Computer Science 74 ( 2015 ), 43-46
- S. Arumugam and J. Saral, Identification of Bottleneck Elements in Cellular Manufacturing Problem, Procedia Computer Science, 74 ( 2015 ), 181-185.
- S. Arumugam, S.T. Hedetniemi, S.M. Hedetniemi, L. Sathikala and S. Sudha, The Covering Chain of a Graph, Utilitas Math., 98 (2015), 183-196. 2016
- S. Arumugam, N. Kamatchi and P. Kovar, Distance Magic Graphs, Utilitas Math., 99 (2016), 131-142.
- S. Arumugam, Kiran Bhutani and L. Sathikala, On (r,s)-fuzzy Domination in Fuzzy Graphs, New Mathematics and Natural Computation, 12(1) (2016), 1-10.
- Neil Buckley, Atulya K Nagar and S. Arumugam, On Real-valued Visual Cryptographic Basis Matrices, Journal of Universal Computer Science, 21(12) (2015), 1536-1562.
- Jessica Pereira, T. Singh and S. Arumugam, m-Gracefulness of Graphs, Algorithms and Discrete Applied Mathematics, In CALDAM 2016, S. Govindarajan and A. Maheshwari (Eds.), Lecture Notes in Comput. Sci., 9602 (2016), 289-298.
- R. Lakshmanan and S. Arumugam, Construction of a (k, n)-visual cryptography scheme, Des. Codes Cryptogr., DOI 10.1007/s10623-016-0181-z
- Neil Buckley, Atulya K. Nagar and S. Arumugam, On the use of secret sharing as a secure cipher, Special issue on Innovations in Systems and Software Engineering: A NASA Journal, DOI 10.1007/s11334-016-0273-y.

**Accepted Papers:**

- S. Arumugam and R. Anantha Kumar, Distance Similar Sets in Graphs, Utilitas Math., (Accepted)
- S. Arumugam and M. Nalliah, Super (a, 3)-edge-antimagic total labeling for union of two stars, Utilitas Math., (Accepted)
- B. Vasanthi, S. Arumugam, and S.V. Nayana, Personal Sharing in Small Groups-A Case Study, Proceedia-Social and Behavioral Sciences (Accepted)
- Neil Buckley, Atulya K. Nagar and S. Arumugam, On Real-valued Visual Cryptographic Basis Matrices, Journal of Universal Computer Science (Accepted)
- SV. Divya Rashmi, A. Somasundram and S. Arumugam, Upper Secure Domination in Graphs, Electronic Notes in Discrete Mathematics (Accepted)
- S. Arumugam, Purnima Gupta and Rajesh Singh, Bounds on Graphoidal Length of a Graph, Electronic Notes in Discrete Mathematics (Accepted)
- S. Arumugam, J. Saral and A. Somasundaram, Minimizing the Number of Exceptional Edges in Cellular Manufacturing Problem, Electronic Notes in Discrete Mathematics (Accepted)
- M. Indumathy, S. Arumugam, Veeky Baths and T. Singh, Graph Theoretic Concepts in the Study of Biological Networks, Applied Analysis with Applications in Biological and Physical Sciences, Springer (Accepted)
- S. Arumugam, J. Saral and Ashwin Ganesan, Decomposition of Bipartite Graphs Arising in Cellular Manufacturing Systems, Int. J. Advance. Soft Comput. Appl., (Accepted)
- R. Kanniga Devi, K. Vimala Devi, and S. Arumugam, Dynamic Batch Mode Cost-efficient Independent Task Scheduling Scheme in Cloud Computing, Int. J. Advance. Soft Comput. Appl., (Accepted)
- S. Arumugam, S. Sriram, D. Ranganayakulu, Ibrahim Venkat and K.G. Subramanian, Eccentric Digraphs of Tournaments, Int. J. Advance. Soft Comput. Appl., (Accepted)
- S.V. Divya Rashmi, S. Arumugam, and Ibrahim Venkat, Secure Domination and Secure Irredundance in Graphs, Int. J. Advance. Soft Comput. Appl., (Accepted)