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

For a simple graph G = (V, E) with the vertex set V and the edge set E and for an integer k, 2 <= k <= vertical bar E(G)vertical bar, an edge labeling phi : E(G) -> {0, 1, ..., k - 1} induces a vertex labeling phi* : V(G) ->{0, 1, ..., k - 1} defined by phi*(v) = phi(e(1)) . phi(e(2)) ..... phi(e(n)) (mod k), where e(1), e(2), ..., e(n) are the edges incident to the vertex v. The function phi is called a k-total edge product cordial labeling of G if vertical bar(e(phi)(i) + v(phi)*(i)) -(e(phi)(j) + v(phi)*(j))vertical bar <= 1 for every i, j, 0 <= i < j <= k - 1, where e(phi)(i) and v(phi)* (i) are the number of edges and vertices with phi(e) = i and phi*(v) = i, respectively. In this paper, we investigate the 3-total edge product cordial labeling of a carbon nanotube network. (C) 2018 Kalasalingam University. Publishing Services by Elsevier B.V.