Assume we have a set of k colors and we assign an arbitrary subset of these colors to each
vertex of a graph G. If we require that each vertex to which an empty set is assigned has in …

The problem of monitoring an electric power system by placing as few measurement devices
in the system as possible is closely related to the well-known domination problem in graphs …

A coprime labeling of a graph of order $ n $ is an assignment of distinct positive integer
labels in which adjacent vertices have relatively prime labels. Restricting labels to only the …

The chromatic number, χ (G) of a graph G is the minimum number of colors used in a proper
coloring of G. In an improper coloring, an edge uv is bad if the colors assigned to the end …

The problem of monitoring an electric power system by placing as few measurement devices
in the system can be formulated as a power dominating set problem in graph theory. The …

A graph G is called prime if the vertices of G can be assigned distinct labels 1, 2,…,| V (G)|
such that the labels on any two adjacent vertices are relatively prime. By showing that for …

We consider the weakly convex and convex domination numbers for two classes of graphs:
generalized Petersen graphs and flower snark graphs. For a given generalized Petersen …

We discuss in this paper the independence numbers and algebraic properties of I-graphs.
The I-graphs are a further generalization of the Generalized Petersen graphs whose …

In this paper, we study the independence number of various classes of I-graphs. I-graphs
are generalizations of the Generalized Petersen Graphs. We provide constructions of …

Suppose V is a finite set and C a collection of subsets of V that contains∅ and V and is
closed under taking intersections. Then the ordered pair (V, C) is called a convexity and the …