Effect of vertex deletion on the weak Roman domination number of a graph
P. Roushini Leely Pushpam, M. Kamalam · AKCE International Journal of Graphs and Combinatorics · 2018
Let be a graph and be a function. The weight of a vertex is and a vertex with weight is said to be undefended with respect to , if it is not adjacent to a vertex with positive weight. The function is a weak Roman dominating function (WRDF) if each vertex with is adjacent to a vertex with such that the function defined by , and if , has no undefended vertex. The weight of is . The weak Roman domination number, denoted by , is the minimum weight of a weak Roman dominating function on . In this paper we examine the effects on when is modified by deleting a vertex.