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ON THE INDEPENDENT DOM-SATURATION NUMBER OF A GRAPH
Keywords:
domination, independent domination, independence, independent dom-saturation numberDOI:
https://doi.org/10.17654/0974165826003Abstract
Let $i s(v, G)$ denote the minimum cardinality among all maximal independent sets of $G$ containing $v$. Then $\operatorname{is}(G)=\max \{i s(v): v \in V(G)\}$ is called the independent dom-saturation number of $G$. In this paper, we study the effect of removal of an edge on the independent dom-saturation number of a graph. We also study the concept of $i s$-subdivision number of a graph and initiate a study of edge independent dom-saturation number of a graph $G$.
Received: July 13, 2025
Accepted: October 24, 2025
References
[1] B. D. Acharya, The strong domination number of a graph and related concepts, J. Math. Phys. Sci. 14(5) (1980), 471-475.
[2] S. Arumugam, On three domination related parameters of a graph, Proceedings of the Conference on Graph Connections, R. Balakrishnan, H. M. Mulder and A. Vijayakumar, eds., Allied Publishers Ltd., 1998, pp. 41-43.
[3] S. Arumugam, O. Favaron and S. Sudha, Irredundance saturation number of a graph, Australas. J. Combin. 46 (2010), 37-49.
[4] S. Arumugam and R. Kala, Domsaturation number of a graph, Indian J. Pure Appl. Math. 33(11) (2002), 1671-1676.
[5] S. Arumugam and J. Paulraj Joseph, Domination in subdivision graphs, J. Indian Math. Soc. 62 (1996), 274-282.
[6] S. Arumugam and M. Subramanian, Edge subdivision and independence saturation in a graph, Graph Theory Notes N. Y. 52 (2007), 9-12.
[7] S. Arumugam and M. Subramanian, Independence saturation and extended domination chain in graphs, AKCE J. Graphs. Combin. 4(2) (2007), 171-181.
[8] J. R. Carrington, F. Harary and T. W. Haynes, Changing and unchanging the domination number of a graph, J. Combin. Math. Combin. Comput. 9 (1991), 57-63.
[9] F. Harary, Changing and unchanging invariants for graphs, Bull. Malaysian Math. Soc. 5 (1982), 73-78.
[10] T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, Inc., New York, 1998.
[11] F. Harary, Graph Theory, Addison-Wesley, Reading, Mass, 1972.
[12] T. Muthulakshmi and M. Subramanian, A characterization of the extended DII-sequence, J. Discrete Math. Sci. Cryptogr. 17(1) (2014), 1-17.
[13] T. Muthulakshmi and M. Subramanian, Independence saturation number of some classes of graphs, Far East J. Math. Sci. (FJMS) 86(1) (2014), 11-21.
[14] T. Muthulakshmi and M. Subramanian, Independent dom-saturation number of a graph, Advances and Applications in Discrete Mathematics 19(1) (2018), 1-16.
[15] M. Subramanian, Studies in graph theory-independence saturation in graphs, Ph.D thesis, Manonmaniam Sundaranar University, Tamilnadu, India, 2004.
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