Central Graph of Quadrilateral Snakes with Chromatic Number

R S Chandel,Rohit Mehta,Akhlak Mansuri

doi:10.22342/jims.27.1.948.1-8

Abstract

This article shows the study about the harmonious coloring and to investigate the harmonious chromatic number of the central graph of quadrilateral snake, double quadrilateral snake, triple quadrilateral snake, k-quadrilateral snake, alternate quadrilateral snake, double alternate quadrilateral snake, triple alternate quadrilateral snake and k-alternate quadrilateral snake, denoted by C(Qn), C(DQn), C(TQn), C(kQn), C(AQn), C(D(AQn)), C(T(AQn)), C(k(AQn)) respectively.

Highlights

The harmonious coloring [6, 7, 8, 17, 18] of a simple graph G is a kind of vertex coloring in which each edge of graph G has different color pair and least number of colors are to be used for this coloring is called the harmonious chromatic number, denoted by χH (G)
For a simple graph G when we subdivide the each edge and connect all the non-adjacent vertices, such obtained graph is called the central graph [7, 17, 18] of G and it is denoted by C(G)
This article shows the study about the harmonious coloring and we find the harmonious chromatic number of central graph of k- quadrilateral and k-alternate quadrilateral snakes χH (C(kQn)) = (3k + 2)n − (3k + 1), and χH (C(k(AQn))) =

Summary

INTRODUCTION

The harmonious coloring [6, 7, 8, 17, 18] of a simple graph G is a kind of vertex coloring in which each edge of graph G has different color pair and least number of colors are to be used for this coloring is called the harmonious chromatic number, denoted by χH (G). For central graph of quadrilateral snake Qn, the harmonious chromatic number, χH (C(Qn)) = 5n − 4, n ≥ 2. Let us consider Qn as the quadrilateral snake graph and Pn as the path graph contains n vertices u1, u2, ..., un. For central graph of double quadrilateral snake DQn, the harmonious chromatic number, χH (C(DQn)) = 8n − 7, n ≥ 2. Let us consider DQn as the double quadrilateral snake and Pn as the path graph with n vertices u1, u2, ..., un. For central graph of triple quadrilateral snake T Qn, the harmonious chromatic number, χH (C(T Qn)) = 11n − 10, n ≥ 2. Let us consider T Qn as the triple quadrilateral snake and Pn as the path graph with n vertices u1, u2, ..., un.

Harmonious Chromatic Number of k-Quadrilateral Snake

Conclusion