Exploring fibonacci cordiality in corona graphs

A Fibonacci cordial (FC) labeling of a graph G is an injective function f : V(G) → {F0, F1, …, Fn}, where Fi is the ith Fibonacci number, such that the induced edge labeling f*(uv) = (f(u) + f(v)) (mod 2) satisfies |ef(0) − ef(1)| ≤ 1. A graph admitting such a labeling is called a Fibonacci cordial. First introduced by Rokad and Ghodasara (2016), FC labeling has been studied for several graph families. Mitra and Bhoumik (2020) extended this to complete graphs, cycles, and their corona (Cn and Kp for p ≤ 3). Motivated to build upon their work, we investigate Cn ⊙ Kp for p ≥ 4. Additionally, we examine whether the aforementioned family of corona graphs retains Fibonacci cordiality when alterations are made to the order of the corona, as observed in the family Kn ⊙ Cm. Moreover, we investigate the conditions under which two additional corona graph families, namely Km ⊙ Km and Kn, n ⊙ Kp, exhibit Fibonacci cordial labeling.