Every branch of mathematics employs some notion of a product that enables the com-
bination or decomposition of its elemental structures. In graph theory there are four main …

Graph theory experienced a tremendous growth in the 20th century. One of the main
reasons for this phenomenon is the applicability of graph theory in other disciplines such as …

Independent domination in graphs: A survey and recent results - ScienceDirect Skip to main
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This chapter is concerned with the concept Roman domination in graphs, which was
introduced in 2004 by Cockayne, Dreyer, SM Hedetniemi, and ST Hedetniemi based on the …

A set S of vertices in a graph G is a paired dominating set if every vertex of G is adjacent to a
vertex in S and the subgraph induced by S contains a perfect matching (not necessarily as …

A total Roman dominating function of a graph G=(V, E) is a function f: V (G)→{0, 1, 2} such
that for every vertex v with f (v)= 0 there exists a vertex u adjacent to v with f (u)= 2, and such …

A Roman dominating function of a graph G=(V, E) is a function f: V→{0, 1, 2} such that every
vertex with f (v)= 0 is adjacent to some vertex with f (v)= 2. The Roman domination number of …

The domination game, played on a graph G, was introduced in Brešar et al.(2010)[2].
Vertices are chosen, one at a time, by two players Dominator and Staller. Each chosen …

A map f: V→ 0, 1, 2 is a Roman dominating function for G if for every vertex v with f (v)= 0,
there exists a vertex u, adjacent to v, with f (u)= 2. The weight of a Roman dominating …

A longest sequence $ S $ of distinct vertices of a graph $ G $ such that each vertex of $ S $
dominates some vertex that is not dominated by its preceding vertices, is called a Grundy …