Abstract

Let $G=V(G),E(G)$ be a graph. A complementary signed edge dominating function $(CSEDF)$ of G is a function $ g: E(G)\rightarrow\{-1,+1\} $ such that $\sum{_{e{^{'}}\notin N[e]}} {g(e^{'})} \geq 1 ,$ for every $e\in E(G)$. Weight of a CSEDF g is defined as $w(g)= \sum{_{e \in E(G)}} {g(e)}$. The complementary signed edge domination number of G is defined as $ \gamma{^{'}}_{cs} {(G)} = min \{ w(g)$ $|$ g is a CSEDF of G\}. In this paper, the complementary signed edge domination number for some graphs are found.

Keywords and Phrases

Dominating function, Signed edge dominating function, Complementary signed edge dominating function.

A.M.S. subject classification

05C69, 05C70.

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