3-Total Edge Product Cordial Labeling for Stellation of Square Grid Graph

Abstract

Let G be a simple graph with vertex set V G and edge set E G . An edge labeling δ : E G ⟶ 0,1 , … , p − 1 , where p is an integer, 1 ≤ p ≤ E G , induces a vertex labeling δ ∗ : V H ⟶ 0,1 , … , p − 1 defined by δ ∗ v = δ e 1 δ e 2 ⋅ δ e n mod p , where e 1 , e 2 , … , e n are edges incident to v . The labeling δ is said to be p -total edge product cordial (TEPC) labeling of G if e δ i + v δ ∗ i − e δ j + v δ ∗ j ≤ 1 for every i , j , 0 ≤ i ≤ j ≤ p − 1 , where e δ i and v δ ∗ i are numbers of edges and vertices labeled with integer i , respectively. In this paper, we have proved that the stellation of square grid graph admits a 3-total edge product cordial labeling.