On 3-total edge product cordial labeling of grid

Abstract

Let us consider a mapping [Formula: see text] of a graph [Formula: see text], where [Formula: see text] is an integer, [Formula: see text]. The mapping [Formula: see text] induces for every vertex [Formula: see text] of [Formula: see text] the label [Formula: see text]. Let [Formula: see text] ([Formula: see text]) denote the number of edges (vertices) in [Formula: see text] that are labeled with the number [Formula: see text] under the labeling [Formula: see text], [Formula: see text].The function [Formula: see text] is called a [Formula: see text]-total edge product cordial labeling of [Formula: see text] if [Formula: see text] for [Formula: see text]. A graph [Formula: see text] with a [Formula: see text]-total edge product cordial labeling is called a [Formula: see text]-total edge product cordial graph.In this paper, we prove that the grid graph [Formula: see text] for [Formula: see text] admits a [Formula: see text]-total edge product cordial labeling.