4-total edge product cordial for some star related graphs

Abstract

Let G = (V (G), E(G)) be a graph, define an edge labeling function ψ from E(G) to {0, 1,..., k − 1} where k is an integer, 2 ≤ k ≤ |E(G)|, induces a vertex labeling function ψ∗ from V (G) to {0, 1,..., k − 1} such that ψ∗(v) = ψ(e1) × ψ(e2) ×... × ψ(en) mod k where e1, e2,..., en are all edge incident to v. This function ψ is called a k-total edge product cordial (or simply k-TEPC) labeling of G if the absolute difference between number of vertices and edges labeling with i and number of vertices and edges labeling with j no more than 1 for all i, j ∈ {0, 1,..., k − 1}. In this paper, 4-total edge product cordial labeling for some star related graphs are determined.