Domination in Jahangir graph J_{2,m}

Abstract

Given graph G = (V, E), a dominating set S is a subset of vertex set V such that any vertex not in S is adjacent to at least one vertex in S. The domination number of a graph G is the minimum size of the dominating sets of G. In this paper we study some results on domination number, connected, independent, total and restrained domination number denoted by γ(G), γ c (G) ,γ i (G), γ t (G) and γ r (G) respectively in Jahangir graphs J 2,m .

The Wiener Index and the Hosoya Polynomial of the Jahangir Graphs

“…Definition 2.1. [23,24] The Jahangir graphs Jn,m is a graph on nm+1 vertices and m(n+1) edges  n≥2 &  m≥3; i.e., a graph consisting of a cycle Cnm with one additional vertex which is adjacent to m vertices of Cnm at distance n to each other on Cnm. In particular,  m≥3 the Jahangir graphs J5,m is a graph consisting of a cycle C5m with one additional vertex (the Center vertex c) which is adjacent to m vertices of Cnm at distance 5 to each other on C5m.…”

Some Invariants of Jahangir Graphs

“…In [12], Laurdusamy et al computed the pebbling number of Jahangir graph J 2,m for m ≥ 8. Mojdeh et al in [13] computed domination number in J 2,m and Ramsey number for J 3,m in [14] ( ) The first topological index was introduced by Wiener [18] and it was named path number, which is now known as Wiener index. In chemical graph theory, this is the most studied molecular topological index due to its wide applications, see for details [19,20].…”

Some results on cordiality labeling of generalized Jahangir graph

“…For n, m ≥ 2, the generalized Jahangir graph J n,m is a graph on nm + 1 vertices, that is, the graph consists of a cycle C mn with one additional vertex which adjacent to a m vertices of C mn at distance n to each other on C mn , see [1,7]. The following figure shows the graph J n,m for n = 3 and m = 10.…”