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

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,"

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.