Strong Split Independent Domination in Fuzzy Graphs

Abstract

An independent dominating set D of a fuzzy graph $G=(\sigma, \mu)$ is a split dominating set if the induced subgraph $H=(\langle V-D\rangle, \sigma', \mu')$ is disconnected. The minimum of the fuzzy cardinalities of a split independent dominating sets of G is called the split independent domination number $\gamma_{sif}(G)$ of G. An independent dominating set D of a fuzzy graph $G=(\sigma, \mu)$ is a strong split independent dominating set if the induced subgraph $H=(\langle V-D\rangle, \sigma', \mu')$ is totally disconnected. The minimum of the fuzzy cardinalities of a strong split independent dominating sets of G is called the strong split independent domination number $\gamma_{ssif}(G)$ of G. In this paper we study a strong split independent dominating sets of fuzzy graphs and investigate the relationship of $\gamma_{ssif}(G)$ or $\gamma_{ssif}$ with other known parameter of G.