3-total edge product cordial labeling of rhombic grid

Abstract

For a simple graph G=(V(G),E(G)), this paper deals with the existence of an edge labeling χ:E(G)→{0,1,…,k−1},2≤k≤|E(G)|, which induces a vertex labeling χ∗:V(G)→{0,1,…,k−1} in such a way that for each vertex v, assigns the label χ(e1)⋅χ(e2)⋅⋯⋅χ(en)((modk)), where e1,e2,…,en are the edges incident to the vertex v. The labeling χ is called a k-total edge product cordial labeling of G if |(eχ(i)+vχ∗(i))−(eχ(j)+vχ∗(j))|≤1 for every i,j,0≤i<j≤k−1, where eχ(i) and vχ∗(i) are the number of edges and vertices with χ(e)=i and χ∗(e)=i, respectively. In this paper, we examine the existence of such labeling for rhombic grid graph.