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

Abstract

We assume finite, simple and undirected graphs in this study. Let G, H be two graphs. By an (a,d)-H- antimagic total graph, we mean any obtained bijective function 𝑓 ∶ 𝑉 ( 𝐺 ) ∪ 𝐸 ( 𝐺 ) → {1, 2, 3, … , | 𝑉 ( 𝐺 )| + | 𝐸 ( 𝐺 )| } such that for each subgraph H’ which is isomorphic to H, their total H-weights 𝑤(𝐻) = ∑ 𝑓(𝑣) 𝑣∈𝐸 ( 𝐻 ′ ) + ∑ 𝑓(𝑒) show an arithmetic sequence {𝑎, 𝑎 + 𝑑, 𝑎 + 2𝑑, … . , 𝑎 + (𝑚 − 1)𝑑} where a, d > 0 are integers and m is the cardinality of all subgraphs H’ isomorphic to H. An (a, d)-H-antimagic total 𝑣∈𝐸 ( 𝐻 ′ ) labeling f is called super if the smallest labels are assigned in the vertices. In this paper, we will study a super (a, d)-B m -antimagicness of a connected and disconnected generalized amalgamation of fan graphs in which a path is a terminal.