A Study of Fibonacci Cordial Labeling in Structured Graph Families

Sarbari Mitra; Soumya Bhoumik

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arXiv · 2509.01823

A Study of Fibonacci Cordial Labeling in Structured Graph Families

Sarbari Mitra·Soumya Bhoumik

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Abstract

A \emph{Fibonacci cordial labeling} of a graph $ G $ is an injective function $ f: V(G) \rightarrow \{F_0, F_1, \dots, F_n\} $, where $ F_i $ denotes the $ i^{\text{th}} $ Fibonacci number, such that the induced edge labeling $ f^*: E(G) \rightarrow \{0,1\} $, given by $ f^*(uv) = (f(u) + f(v)) $ $(\bmod\ 2)$, satisfies the balance condition $ |e_f(0) - e_f(1)| \le 1 $. Here, $ e_f(0) $ and $ e_f(1) $ represent the number of edges labeled 0 and 1, respectively. A graph that admits such a labeling is termed a \emph{Fibonacci cordial graph}. In this paper, we investigate the existence and construction of Fibonacci cordial labelings for several families of graphs, including \emph{Generalized Petersen graphs}, \emph{open and closed helm graphs}, \emph{joint sum graphs}, and \emph{circulant graphs of small order}. New results and examples are presented, contributing to the growing body of knowledge on graph labelings inspired by numerical sequences.

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Sarbari Mitra, Soumya Bhoumik. 2025-09-01. A Study of Fibonacci Cordial Labeling in Structured Graph Families. https://arxiv.org/abs/2509.01823

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