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

Abstract

For a simple graph G=(V,E)with the vertex set Vand the edge set Eand 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,…,enare 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. Keywords: Cordial labeling, k-total edge product cordial labeling, Carbon nanotube network