In this paper, we introduce a suitable generalization of Cayley graphs that is defined over polygroups (GCP-graph) and give some examples and properties. Then, we mention a generalization of NEPS that contains some known graph operations and apply to GCP-graphs. Finally, we prove that the product of GCP-graphs is again a GCP-graph.

modeling of network security is useful approach to comprehend the status. In this paper, network is modeled in a graph. Security problem is solved in graph as Graph Coloring Problem (GCP). In GCP, two adjacent nodes must have different colors. Thus GCP provides the security in the network. One objective in GCP is chromatic number and another objective is total price. We present a multi-objectiv...

In graph theory, Graph Colouring Problem (GCP) is an assignment of colours to vertices of any given graph such that the colours on adjacent vertices are different. The GCP is known to be an optimization and NP-hard problem. Imperialist Competitive Algorithm (ICA) is a meta-heuristic optimization and stochastic search strategy which is inspired from socio-political phenomenon of imperialistic co...

This paper provides an insight into graph coloring application of the contemporary heuristic methods. It discusses a variety algorithmic solutions for The Graph Coloring Problem (GCP) and makes recommendations implementation. GCP is NP-hard problem, which aims at finding minimum number colors vertices in such way, that none two adjacent are marked with same color.With advent multicore processin...

This paper presents an analysis of solutions of the Graph Coloring Problem (GCP). Given an undirected graph G(V,E) with a vertex set V and an edge set E, the goal of GCP is to find a color assignment to every vertex in V such that any pair of adjacent (or connected) vertices receive different colors, and the total number of colors required for the feasible color assignment be minimized; the sma...

This paper proposes a new method based on the cultural algorithm to solve graph coloring problem (GCP). Graph coloring problem involves finding the minimum number of colors for coloring the graph vertices such that adjacent vertices have distinct colors. In this paper various components of cultural algorithm have been implemented to solve GCP with a self adaptive behavior in an efficient manner...

This paper proposes a new method based on the cultural algorithm to solve graph coloring problem (GCP). Graph coloring problem involves finding the minimum number of colors for coloring the graph vertices such that adjacent vertices have distinct colors. In this paper various components of cultural algorithm have been implemented to solve GCP with a self adaptive behavior in an efficient manner...

Given an undirected graph G=(V ,E), the Graph Coloring Problem (GCP) consists in assigning a color to each vertex of the graph G in such a way that any two adjacent vertices are assigned different colors, and the number of different colors used is minimized. State-of-the-art algorithms generally deal with the explicit constraints in GCP: any two adjacent vertices should be assigned different co...

The graph coloring problem (GCP) is one of the most studied NP hard problems and has numerous applications. Despite the practical importance of GCP, there are limited works in solving GCP for very large graphs. This paper explores techniques for solving GCP on very large real world graphs. We first propose a reduction rule for GCP, which is based on a novel concept called degree bounded indepen...