ON FIBONACCI CORDIAL LABELING OF SOME PLANAR GRAPHS

ON FIBONACCI CORDIAL LABELING OF SOME PLANAR GRAPHS

S. Mitra, A. Pritchard, S. Bhoumik

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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).

Keywords

Fibonacci Cordial labelling, Comb graph, Jellyfish, coconut tree, H−graph, W−graph.