Some New Results on Domination Integrity of Graphs
Affiliation(s)
Saurashtra University, Rajkot, India. B. H. Gardi college of Engineering & Technology, Rajkot, India.
Saurashtra University, Rajkot, India. B. H. Gardi college of Engineering & Technology, Rajkot, India.
ABSTRACT
The domination integrity of a connected graph G= (V(G), E(G)) is denoted as DI(G) and defined by DI(G) = min{*S*+ m(G-S) : S is a dominating set } where m(G-S) is the order of a maximum component of G-S . We discuss domination integrity in the context of some graph operations like duplication of an edge by vertex and duplication of vertex by an edge.
The domination integrity of a connected graph G= (V(G), E(G)) is denoted as DI(G) and defined by DI(G) = min{*S*+ m(G-S) : S is a dominating set } where m(G-S) is the order of a maximum component of G-S . We discuss domination integrity in the context of some graph operations like duplication of an edge by vertex and duplication of vertex by an edge.
Cite this paper
S. Vaidya and N. Kothari, "Some New Results on Domination Integrity of Graphs," Open Journal of Discrete Mathematics, Vol. 2 No. 3, 2012, pp. 96-98. doi: 10.4236/ojdm.2012.23018.
S. Vaidya and N. Kothari, "Some New Results on Domination Integrity of Graphs," Open Journal of Discrete Mathematics, Vol. 2 No. 3, 2012, pp. 96-98. doi: 10.4236/ojdm.2012.23018.
References
[1] C. A. Barefoot, R. Entringer and H. C. Swart, “Vulnerability in Graphs—A Comparative Survey,” Journal of Combinatorial Mathematics and Combinatorial Computing, Vol. 1, 1987, pp. 13-22. [2] A. Mamut and E. Vumar, “A Note on the Integrity of Middle Graphs,” Lecture Notes in Computer Science, Vol. 4381, 2007, pp. 130-134. [3] P. Dundar and A. Aytac, “Inte-grity of Total Graphs via Certain Parameters,” Mathematical Notes, Vol. 75, No. 5, 2004, pp. 665-672. [4] R. Sundares-waran and V. Swaminathan, “Domination Integrity in Graphs,” Proceedings of International Conference on Mathematical and Experimental Physics, Prague, 3-8 August 2009, pp. 46-57. [5] R. Sundareswaran and V. Swaminathan, “Domina-tion Integrity of Middle Graphs,” In: T. Chelvam, S. Somasun-daram and R. Kala, Eds., Algebra, Graph Theory and Their Applications, Narosa Publishing House, New Delhi, 2010, pp. 88-92. [6] T. Haynes, S. Hedetniemi and P. Slater, “Funda-mentals of Domination in Graphs,” Marcel Dekker, Inc., New York, 1998.
[1] C. A. Barefoot, R. Entringer and H. C. Swart, “Vulnerability in Graphs—A Comparative Survey,” Journal of Combinatorial Mathematics and Combinatorial Computing, Vol. 1, 1987, pp. 13-22. [2] A. Mamut and E. Vumar, “A Note on the Integrity of Middle Graphs,” Lecture Notes in Computer Science, Vol. 4381, 2007, pp. 130-134. [3] P. Dundar and A. Aytac, “Inte-grity of Total Graphs via Certain Parameters,” Mathematical Notes, Vol. 75, No. 5, 2004, pp. 665-672. [4] R. Sundares-waran and V. Swaminathan, “Domination Integrity in Graphs,” Proceedings of International Conference on Mathematical and Experimental Physics, Prague, 3-8 August 2009, pp. 46-57. [5] R. Sundareswaran and V. Swaminathan, “Domina-tion Integrity of Middle Graphs,” In: T. Chelvam, S. Somasun-daram and R. Kala, Eds., Algebra, Graph Theory and Their Applications, Narosa Publishing House, New Delhi, 2010, pp. 88-92. [6] T. Haynes, S. Hedetniemi and P. Slater, “Funda-mentals of Domination in Graphs,” Marcel Dekker, Inc., New York, 1998.