On 3-total edge product cordial labeling of a carbon nanotube network

Abstract

For a simple graph G=(V,E) with the vertex set V and the edge set E and for an integer k, 2≤k≤|E(G)|, an edge labeling φ:E(G)→{0,1,…,k−1} induces a vertex labeling φ∗:V(G)→{0,1,…,k−1} defined by φ∗(v)=φ(e1)⋅φ(e2)⋅…⋅φ(en)(modk), where e1,e2,…,en are the edges incident to the vertex v. The function φ is called a k-total edge product cordial labeling of G if |(eφ(i)+vφ∗(i))−(eφ(j)+vφ∗(j))|≤1 for every i,j, 0≤i<j≤k−1, where eφ(i) and vφ∗(i) are the number of edges and vertices with φ(e)=i and φ∗(v)=i, respectively.In this paper, we investigate the 3-total edge product cordial labeling of a carbon nanotube network.