Some New Results on Prime Cordial Labeling

S. K. Vaidya,N. H. Shah

doi:10.1155/2014/607018

Abstract

A prime cordial labeling of a graph G with the vertex set V(G) is a bijection f:V(G)→{1,2,3,…,|V(G)|} such that each edge uv is assigned the label 1 if gcd(f(u),f(v))=1 and 0 if gcd(f(u),f(v))>1; then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. A graph which admits a prime cordial labeling is called a prime cordial graph. In this work we give a method to construct larger prime cordial graph using a given prime cordial graph G. In addition to this we have investigated the prime cordial labeling for double fan and degree splitting graphs of path as well as bistar. Moreover we prove that the graph obtained by duplication of an edge (spoke as well as rim) in wheel Wn admits prime cordial labeling.

Highlights

We consider a finite, connected, undirected, and simple graph G = (V(G), E(G)) with p vertices and q edges which is denoted as G(p, q)
If G1 is the graph obtained by identifying the vertices V1 and V2 of K2,n with the vertices of G having labels 2 and 4, respectively, G1 admits prime cordial labeling in any of the following cases: (i) n is even and G is of any size q; (ii) n, p, and q are odd with ef(0) = ⌊q/2⌋; (iii) n is odd, p is even, and q is odd with ef(0) = ⌈q/2⌉
A new approach for constructing larger prime cordial graph from the existing prime cordial graph is investigated

Summary

Introduction

A prime cordial labeling of a graph G with vertex set V(G) is a bijection f : V(G) → {1, 2, 3, . If G1 is the graph obtained by identifying the vertices V1 and V2 of K2,n with the vertices of G having labels 2 and 4, respectively, G1 admits prime cordial labeling in any of the following cases: (i) n is even and G is of any size q; (ii) n, p, and q are odd with ef(0) = ⌊q/2⌋; (iii) n is odd, p is even, and q is odd with ef(0) = ⌈q/2⌉.

Results

Conclusion