A Note on the Hop Domination Number of a Subdivision Graph

Abstract

Let G = (V, E) be a graph with p vertices and q edges. A subsetThe minimum cardinality of a hop dominating set of G is called a hop domination number of G and is denoted by γ h (G). The subdivision graph S(G) of a graph G is a graph obtained by subdividing every edge of G exactly once. In this paper, we obtain an upper bound on hop domination number of subdivision graph of any connected graph G in terms of number of edges q, the maximum degree ∆(G) and domination number γ(G) of G. We also characterize the family of connected graphs attaining this bound.

A Novel Domination in Vague Influence Graphs with an Application

“…Mathew et al [20,21] expressed the notions of fuzzy end vertices for In-FGs. Natarajan et al [22] studied strong (weak) domination in FGs. Certain properties of domination in VG products were explained by Shi et al [23].…”

Some Properties of Zero Forcing Hop Dominating Sets in a Graph

“…is the closed hop neighborhood of S in G. The minimum cardinality among all hop dominating sets in G, denoted by γ h (G), is called the hop domination number of G. This concept had been studied on different types of graphs and graph theorists found some interesting results (see [1,2,10]). Since then, several researchers had studied this concepts and they had extended this parameter by introducing variants, that is, imposing additional properties or conditions on the standard hop domination (see [3][4][5][6][7][8][9]11]).…”

Grundy Total Hop Dominating Sequences in Graphs

“…Recently, hop domination was defined and studied by Natarajan and Ayyaswamy in [17]. From then on a lot of investigations of the concept and some of its variants have been done (see [1,2,[8][9][10][11][12][13][14][15]20]).…”