Dominating Number on Icosahedral-Hexagonal Network

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].  

Geometric Properties of the Icosahedral-Hexagonal Grid on the Two-Sphere

An icosahedral-hexagonal grid on the two-sphere is created by dividing the faces of an icosahedron and projecting the vertices onto the sphere. This grid and its Voronoi tessellation have several desirable features for numerical simulations of physical processes on the sphere. While several methods to construct the icosahedral grid mesh have been proposed over the past decades, and empirical da...

On the Number of k-Dominating Independent Sets

We study the existence and the number of k-dominating independent sets in certain graph families. While the case k = 1 namely the case of maximal independent sets which is originated from Erdős and Moser is widely investigated, much less is known in general. In this paper we settle the question for trees and prove that the maximum number of kdominating independent sets in n-vertex graphs is bet...

Bounding and dominating number of families of functions on N

We pursue the study of families of functions on the natural numbers, with emphasis here on the bounded families. The situation being more complicated than the unbounded case, we attack the problem by classifying the families according to their bounding and dominating numbers, the traditional scheme for gaps. Many open questions remain.

On maximum number of minimal dominating sets in graphs