Fibonacci Divisor Cordial Graphs

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 $f : V \rightarrow \{F_1, F_2,F_3,\dots ,F_p\}$, 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 paper, we prove that the graphs $P_n$, $C_n$, $K_{2,n} \odot u_2(K_1)$ and subdivision of bistar(\textless $B_ {n,n}:w>)$ are Fibonacci divisor cordial graphs. We also prove that $K_n(n\geq 3)$ is not Fibonacci divisor cordial graph.