A Fibonacci cordial labeling of a graph \ (G\) is an injective function \ (f: V (G) \F₀, F₁, , \\ Fₙ\\), where \ (Fᵢ\) denotes the \ (i^th\) Fibonacci number, such that the induced edge labeling \ (f^*: E (G) \0, 1\\), given by \ (f^* (uv) = (f (u) + f (v) ) \) \ ( (\ 2) \), satisfies the balance condition \ (|ef (0) - ef (1) | 1\). Here, \ (ef (0) \) and \ (ef (1) \) represent the number of edges labeled 0 and 1, respectively. A graph that admits such a labeling is termed a Fibonacci cordial graph. In this paper, we investigate the existence and construction of Fibonacci cordial labelings for several families of graphs, including Generalized Petersen graphs, open and closed helm graphs, joint sum graphs, and 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.
Mitra et al. (Sun,) studied this question.