In this paper, we further study the concepts of hop domination and 2-step domination and
introduce the concepts of restrained hop domination, total restrained hop domination, 2-step …

In a graph G, a set D⊆ V (G) is a 2-point set dominating set (in short 2-psd set) of G if for
every subset S⊆ V− D there exists a nonempty subset T⊆ D containing at most two vertices …

Graphs considered here are simple, finite and undirected. A graph is denoted by G and its
vertex set by V (G) and edge set by E (G). Many researchers were attracted by two concepts …

A set D⊆ V of a connected graph G=(V, E) is called a fair detour dominating set if D is a
detour dominating set and every two vertices not in D has same number of neighbors in D …

In secure domination [AP Burger, MA Henning and JH Van Vuuren, Vertex covers and
secure domination in graphs, Quaest Math. 31 (2008) 163–171; EJ Cockayne …

In a simple, finite undirected graph, a dominating set is a subset of the vertex set whose
closed neighbourhood is. Many types of domination have been studied. The studies are …

The basic intention of this paper is to impart the importance of Nano topology induced by
graph. Nano topology induced by graph paves us a method to find the well-known …