Let G=(V, E) be a graph with vertex set V and edge set E. A Roman dominating function is a
mapping f: V→{0, 1, 2} such that every vertex u for which f (u)= 0 is adjacent to at least one …

In this paper, a study has been started on a new variation of the problem on signed roman
domination called signed roman star edge dominance problem. A mapping g: E→{− 1, 1, 2} …

A labeling of a graph is a mapping that maps some set of graph elements to a set of
numbers. In this paper, two new variations of labeling named $ k $-distant edge total …

A labeling of a graph is a mapping that maps some set of graph elements to a set of
numbers (usually positive integers). For a simple graph G=(V, E) with vertex set V and edge …