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) → {1; 2;⋯ |V (G)| + |E(G)|}, such that for all subgraphs P2 ▹; H of G isomorphic to H, then graph G is called an (a; d)-P2 ▹; H- antimagic total graph. Furthermore, we can consider the total P2 B H-weights W(P2 ▹; H) = σv2V (P2BH) f(v) +σe2E(P2▹;H) f(e) which should form an arithmetic sequence {a; a + d; a + 2d; ⋯ a + (n - 1)d}, where a and d are positive integers and n is the number of all subgraphs isomorphic to H. Our paper describes the existence of super (a; d)-P2 ▹; H antimagic total labeling for graph operation of comb product namely of G = L ▹; H, where L is a (b; d?)-edge antimagic vertex labeling graph and H is a connected graph.