Edge k-Product Cordial Labeling of Graphs

Abstract

In this paper, we introduce a new labeling namely ‘edge k-product cordial labeling’ as follows: For a graph G = (V (G), E(G)) having no isolated vertex, an edge labeling f : E(G) → {0, 1, ..., k − 1}, where k > 1 is an integer, is said to be an edge k-product cordial labeling if it induces a vertex labeling f* : V (G) → {0, 1, ..., k − 1} defined by f*(v) = Quv∈E(G) f(uv)(mod k) satisfies |ef(i) − ef(j)| ≤ 1 and |vf*(i) − vf*(j)| ≤ 1 for i, j ∈ {0, 1, ..., k − 1}, where ef(i) and vf*(i) denote the number of edges and vertices respectively having a label i (i = 0, 1, ..., k − 1). Further, we study the edge k-product cordial behavior of star, bistar, shadow and splitting graph of star, path union of star, bistar and cycle graphs.