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