Chromatic Pendant Domination in Graphs

Abstract

Let G=(V,E) be a undirected, simple,finite graph. A subset S of V is said to be dominating set if for every v in V-D there exist u in D such that u and v are adjacent. A dominating set S in G is said to be a pendant dominating set if induced subgraph of S contains at least one pendant vertex. We introduce the concept of chromatic pendant dominating set. A subset S of V is said to be chromatic pendant dominating set if S is a pendant dominating set and $\chi (<S>)= \chi (G)$, where $\chi (G)$ is a chromatic number of G. The minimum cardinality of the chromatic pendant dominating set in $G$ is called the chromatic pendant domination number of G, denoted by \gamma_{cpe}(G)$. We find the chromatic pendant domination number of some standard graphs and characterize the graph for $\gamma_{cpe}(G)=2$