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Wheels are Cycle-Antimagic

2015; Elsevier BV; Volume: 48; Linguagem: Inglês

10.1016/j.endm.2015.05.003

1571-0653

Andrea Semaničová–Feňovčíková, Martin Bača, Marcela Lascśaková, Mirka Miller, Joe Ryan,

Photochromic and Fluorescence Chemistry

A simple graph G admits an H-covering if every edge in E(G) belongs to a subgraph of G isomorphic to H. An (a, d)-H-antimagic total labeling of a graph G admitting an H-covering is a bijective function from the vertex set V(G) and the edge set E(G) of the graph G onto the set of integers {1,2,…,|V(G)|+|E(G)|} such that for all subgraphs H′ isomorphic to H, the sum of labels of all the edges and vertices belonging to H′ constitute the arithmetic progression with the initial term a and the common difference d. Such a labeling is called super if the smallest possible labels appear on the vertices. In this paper, we investigate the existence of super cycle-antimagic total labelings of wheel.