A Study on Odd Prime Labeling of Octopus Graphs Families

An odd prime labeling of a graph G (V,E), is defined as a bijective function f mapping the vertex set V to the set {1,3,5,…,2|V(G)|1}, such that for every edge uvE. the greatest common divisor gcd(f(u),f(v))=1. A graph that permits such a labeling is referred to as an odd prime graph. In this study, we explore the odd prime labeling properties of various graph structures, including the octopus chain graph, octopus ladder graph, twisted octopus ladder graph, and hexa-octopus chain graph.