On Super (a, d)-H-Antimagic Total Covering of Star Related Graphs

摘要

Let G = (V (G),E(G)) be a simple graph and H be a subgraph of G. G admits an H-covering, if every edge in E(G) belongs to at least one subgraph of G that is isomorphic to H. An (a, d)-H-antimagic total labeling of G is a bijection λ: V (G) ∪ E(G) → {1, 2, 3, . . , |V (G)| + |E(G)|} such that for all subgraphs H′ isomorphic to H, the H′ weights constitute an arithmetic progression a, a+d, a+2d, . . , a+(n?1)d where a and d are positive integers and n is the number of subgraphs of G isomorphic to H. Additionally, the labeling λ is called a super (a, d)-H-antimagic total labeling if λ(V (G)) = {1, 2, 3, . . , |V (G)|}. In this paper we study super (a, d)-H-antimagic total labelings of star related graphs G_(u)[S_(n)] and caterpillars.