Super (a, d)-Cycles-Antimagic Labeling of Subdivision of a Fan Graph

Abstract

We consider a simple, connected and undirected graph ( )EVG , with vertex set ()GV and edge set ( ).GE There is a super ( ) H-, da - antimagic total labeling on the graph ( )EVG , if there exists a bijection { }EVEVf +→ ...,,2,1: ∪ such that for all subgraphs isomorphic to H, the total H-weights ( ) =HW ∑∑ () () + efvf form an arithmetic sequence { ( )},1...,,2,, dmadadaa −+++ where 0>a is the smallest value, d is the feasible difference, and m is the number of all subgraphs isomorphic to H. In this paper, we investigate the existence of super ()H-, da -antimagic total labeling for subdivisions of a fan graph (), FS when subgraphs H are cycles.