Some Properties on Strong Roman Domination in Graphs

Abstract

A Strong Roman dominating function (SRDF) is a function satisfying the condition that every vertex for which is adjacent to at least one vertex for which and every vertex for which is adjacent to at least one vertex for which . The weight of an SRDF is the value . The minimum weight of an SRDF on a graph is called the Strong Roman domination numberof . In this paper, we attempt to verify some properties on SRDF and moreover we present Strong Roman domination number for some special classes of graphs. Also we show that for a tree with vertices, leaves and support vertices, we have and we characterize all trees achieving this bound.