On Fibonacci cordial labeling of some planar graphs

Abstract

An injective function f from vertex set V (G) of a graph G to the set {F0, F1, F2, · · · , Fn}, where Fi is the iᵗʰ Fibonacci number (i = 0, 1, · · · , n), is said to be Fibonacci cordial labeling if the induced function f* from the edge set E(G) the set {0, 1} defined by f* (uv) = (f(u) + f(v)) (mod 2) satisfies the condition |ef (0) − ef (1)| ≤ 1, where ef (0) is the number of edges with label 0 and ef (1) is the number of edges with label 1. A graph that admits Fibonacci cordial labeling is called a Fibonacci cordial graph. In this paper we discuss Fibonacci cordial labeling of the families of planar graph (Comb graphs, Coconut trees, Jellyfish Graphs, H−graph and W−graph).