The irredundance number and maximum degree of a graph

The Maximum Number of Edges in a Strongly Multiplicative Graph

Irredundance saturation number of a graph

Let G = (V,E) be a graph and let v ∈ V. Let IRS(v,G) denote the maximum cardinality of an irredundant set in G which contains v. Then IRS(G) = min {IRS(v,G) : v ∈ V } is called the irredundance saturation number of G. In this paper we initiate a study of this parameter.

The Ramsey number of a graph with bounded maximum degree

The Ramsey number of a graph G is the least number t for which it is true that whenever the edges of the complete graph on t vertices are colored in an arbitrary fashion using two colors, say red and blue, then it is always the case that either the red subgraph contains G or the blue subgraph contains G. A conjecture of P. Erdos and S. Burr is settled in the afftrmative by proving that for each...

On the Maximum Number of Dominating Classes in Graph Coloring

In this paper we investigate the dominating- -color number،  of a graph G. That is the maximum number of color classes that are also dominating when G is colored using colors. We show that where is the join of G and H. This result allows us to construct classes of graphs such that and thus provide some information regarding two questions raised in [1] and [2].  

the maximum number of edges in a strongly multiplicative graph

0