Interior Domination on Subdivision and Splitting Graphs of Graphs

Abstract

A subset D of the vertex set $V(G)$ of a graph G is said to be a dominating set if every vertex in V-D is adjacent to some vertex in $D$. A dominating set D is said to be an interior dominating set if every vertex $v\in D$ is an interior vertex of G. The minimum cardinalities among the interior dominating sets of G is called the interior domination number $\gamma_{Id}(G)$ of G. In this paper we discuss interior domination on the subdivision graph $S(G)$ of various graphs.