Prime Cordial Labeling of Contact Networks: An Environmental Application to Epidemic Spread in Aquatic Populations

Abstract

A prime cordial labeling of a graph G is a bijection f:V(G)→{1,2,…,|V(G)|} such that each edge uv∈E(G) is assigned label 1 if gcd(f(u),f(v))=1 and 0 if gcd(f(u),f(v))>1; further the number of edges labeled 0 and 1 differ by at most 1. If a graph admits prime cordial labeling, then it is called a prime cordial graph. We prove that the Durer graph, Heawood graph, Frucht graph, Tietze graph, hypohamiltonian graph, cubic graph with 12 vertices, and crown graph are prime cordial graphs. Also we prove that the Herschel graph, Wagner graph, Moser spindle graph, and truncated tetrahedron graph are not prime cordial graphs.