Edge Antimagic Total Labeling on Two Copies of Path

Abstract

A graph G = (V(G), E(G)) denotes the vertex set and the edge set, respectively. A (p,q)-graph G is a graph such that |V(G) | = p and |E(G) | = q. Graph of order p and size q is called (a,d)-edge-anti magic total if there exists a bijection f : V(G) U E(G)→ {1,2,..., p + q} such that the edge weights w(u,v) = f(u) + f(uv) + f(v) form an arithmetic sequence {a, a + d, a + 2d,...,a + (q – 1)d} with the first term a and common difference d. Two copies of path is disjoint union of two path graph with same order (Pn∪Pn) denoted by 2Pn. In this paper we construct the (a,d)-edge-anti magic total labeling in two copies of path for some differences d.