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 + 2 d ,..., 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 ( P n ∪ P n ) denoted by 2 P n . In this paper we construct the ( a , d )-edge-anti magic total labeling in two copies of path for some differences d.

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