Fibonacci Divisor Cordial Labeling in the Context of Graph Operations on Gr\"{o}tzsch

Fibonacci Divisor Cordial Labeling

Abstract

Let $G = (V, E)$ be a $(p, q)$-graph. A Fibonacci divisor cordial labeling of a graph G with vertex set V is a bijection $f: V \to \{F_{1}, F_{2}, F_{3},\dots, F_{p}\}$, where $F_{i}$ is the $i^{th}$ Fibonacci number such that if each edge $uv$ is assigned the label 1 if $f(u)$ divides $f(v)$ or $f(v)$ divides $f(u)$ and 0 otherwise, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. If a graph has a Fibonacci divisor cordial labeling, then it is called Fibonacci divisor cordial graph. In this research paper, we investigate the Fibancci divisor cordial labeling bahevior for Gr\"{o}tzsch graph, fusion of any two vertices in Gr\"{o}tzsch graph, duplication of an arbitrary vertex in Gr\"{o}tzsch graph, duplication of an arbitrary vertex by an edge in Gr\"{o}tzsch graph, switching of an arbitrary vertex of degree four in Gr\"{o}tzsch graph, switching of an arbitrary vertex of degree three in Gr\"{o}tzsch graph and path union of two copies of Gr\"{o}tzsch.