06081587

j

06081587 Chitra, S. Sattanathan, R. Global vertex-edge domination sets in graph. Int. Math. Forum 7, No. 5-8, 233-240 (2012). 2012 Hikari Ltd., Ruse EN global vertex-edge dominating set global vertex-edge irredundant set global independent vertex-edge domination set global vertex-edge domination chain global vertex-edge domination number

http://www.m-hikari.com/imf/imf-2012/5-8-2012/index.html

Summary: In a graph $G$, a subset $S$ of $V$ is global vertex-edge dominating set if $S$ is vertex-edge dominating set in both $G$ and $\overline G$. In this paper we have introduced new concepts such as global vertex-edge dominating set, global vertex-edge irredundant set, global independent vertex-edge dominating set. We have identified the global vertex-edge domination number of some family of graphs such as $K_{n}$, $K_{1,n-1}$, $K_{n,m}$, $P_n$, and $C_n$. An attempt is made to identify the global vertex-edge domination chain, $$ir_{gve}(G) \leq \gamma_{gve}(G) \leq i_{gve}(G) \leq IR_{gve}(G) \leq \gamma_{gve}(G)$$.