Roman Domination Number of Split Graphs of Certain Graphs

Abstract

A dominating set D in a graph G = (V; E) is a subset of vertices such that every vertex not in D is adjacent to at least one vertex in D. The minimum cardinality of such a set is called the dominating number of G. A Roman dominating function on G is a function f : V ! f0; 1; 2g with the property that every vertex u for which f (u) = 0 is adjacent to at least one vertex v for which f (v) = 2. The weight of a Roman dominating function f is defined as and the minimum possible weight over all Roman dominating functions on G is called the Roman dominating number, denoted by gadjacent to every neighbor of v. In this work, we explore how different graphs relate to their corresponding split graphs S