Strong Efficient Open Domination in Graphs

Abstract

Let $G=(V, E)$ be a simple, undirected, finite graph without isolated vertices. A subset $D$ of $V(G)$ is a {\it Strong(Weak) efficient open dominating set} of $G$ if $\left|N_s(v)\cap D\right|=1$ $(\left|N_w(v)\cap D\right|=1)$, for every $v\in V(G)$ where $N_s(v)$ and $N_w(v)$ are strong and weak neighborhood respectively. The minimum cardinality of $D$ is called as {\it strong(weak) efficient open domination number} and is denoted by $\gamma_{ste}(G)$ $(\gamma_{wte}(G))$ of $G$. A graph $G$ is {\it strong(weak) efficient open dominating graph} if it contains a strong(weak) efficient open dominating set. We write a program to check whether the given graph is strong efficient open dominatable or not in C Language.