The Construction of P2⊳H- antimagic graph using smaller edge - antimagic vertex labeling

Abstract

In this paper we use simple and non trivial graph. If there exist a bijective function g : V (G) [ E(G) ! f1; 2; : : : ; jV (G)j + jE(G)jg, such that for all subgraphs P 2 B H of G isomorphic to H, then graph G is called an (a; d)-P B Hantimagic total graph. Furthermore, we can consider the total P B H-weights W(P 2 B H) = P v2V (P 2 BH) f(v) + P f(e) which should form an arithmetic sequence fa; a + d; a + 2d; :::; a + (n ¡ 1)dg, where a and d are positive integers and e2E(P 2 BH) n is the number of all subgraphs isomorphic to H. Our paper describes the existence of super (a; d)-P B H antimagic total labeling for graph operation of comb product namely of G = L B H, where L is a (b; d 2 ¤ )-edge antimagic vertex labeling graph and H is a connected graph.