A Super (A,D)-Bm-Antimagic Total Covering of Ageneralized Amalgamation of Fan Graphs

Abstract

All graph in this paper are finite, simple and undirected. Let G, H be two graphs. A graph G is said to be an (a,d)-H-antimagic total graph if there exist a bijective function such that for all subgraphs H’ isomorphic to H, the total H-weights form an arithmetic progression where a, d 0 are integers and m is the number of all subgraphs H’ isomorphic to H. An (a, d)-H-antimagic total labeling f is called super if the smallest labels appear in the vertices. In this paper, we will study a super (a, d)-Bm-antimagicness of a connected and disconnected generalized amalgamation of fan graphs on which a path is a terminal.

Keywords

• super (a, d)-bm-antimagic total covering, generalized amalgamation of fan graphs, connected and disconnected