AIJRSTEM19-

2008

Let G = (V,E) be a simple graph. A set S ⊆ V is a dominating set of graph G, if every vertex in V − S is adjacent to at least one vertex in S. The domination number γ(G) is the minimum cardinality of a dominating set in G. It is well known that if e ∈ E(G), then γ(G−e)−1 ≤ γ(G) ≤ γ(G−e). In this paper, as an application of this inequality, we obtain the domination number of some certain graphs.

Discrete Applied Mathematics, 2012

International Journal of Combinatorics, 2012

Discrete Mathematics

arXiv (Cornell University), 2017

Mathematica Slovaca, 2007

The k-restricted domination number of a graph G is the minimum number d k such that for any subset U of k vertices of G, there is a dominating set in G including U and having at most d k vertices. Some new upper bounds in terms of order and degrees for this number are found.

IJCRT, 2019

Let G be a graph with minimal vertex dominating sets G1, G2,……..,Gm. Form a graph D(G) with vertices corresponding to G1, G2, ....,Gm and two sets Gi and Gj are adjacent if they have atleast one vertex in common. This graph D(G) is known as Dominating Graph. Minimum cardinality of a minimal dominating sets of D(G) is called domination number of D(G) and is denoted by γ(D(G)). In this paper, bounds on γ(D(G)) are obtained and its exact values for some standard graphs are found.