The total edge product cordial labeling of graph with pendant vertex

Abstract

One of the topics in graph theory is labeling. The object of the study is a graph generally represented by vertex, edge and sets of natural numbers called label. For a graph G, the function of vertex labeling g : V(G) → {0, 1} induces an edge labeling function g*: E(G) → {0, 1} defined as g*(uv) = g(u)g(v). The function g is called total product cordial labeling of G if |(vg(0) + eg(0)) − (vg(1) + eg(1))| ≤ 1 with vg(0),vg(1),eg(0), and eg(1) respectively are the number of vertex which has label zero, the number of vertex which has label one, the number of edge which has label zero and the number of edge which has label one. All graphs used in this paper are simple and connected graphs. In this paper, we will prove that some graphs with pendant vertex admit total edge product cordial labeling.