Intersection Graph on Non-Split Majority Dominating Graph

J. Joseline Manoraa and S. Veeramanikandanb,*

Intersection Graph on Non-Split Majority Dominating Graph

Authors :

J. Joseline Manora^a and S. Veeramanikandan^b,*

Author Address :

^a,bPG and Research Department of Mathematics, T.B.M.L College, Porayar, 609 307, India.

*Corresponding author.

Abstract :

Let G = (V,E) be a graph. The Minimal Non-Split Majority Dominating Graph MNMD(G) of a graph G is the intersection graph defined on the family of all minimal non-split majority dominating sets of vertices in G and the Common Minimal Non-Split Majority Dominatng Graph CMNMD(G) of a graph G is the graph having the same vertex set as G with two vertices adjacent in CMNMD(G) if and only if there exists a minimal non-split majority dominating set of G containing them. In this article,We have introduced these two concepts and investigated some properties of these graphs. Some characterization theorems are established and bounds of MNMD(G) and CMNMD(G) are also determined.

Keywords :

Minimal Non-Split Majority Dominating Graph MNMD(G), Common Minimal Non-Split Majority Dominating Graph CMNMD(G).

DOI :

Article Info :

Received : August 06, 2015; Accepted : September 28, 2015.