Constructions of H-antimagic graphs using smaller edge-antimagic graphs

Abstract:

A simple graph G - (V, E) admits an H-covering if every edge in E belongs at least to one subgraph of G isomorphic to a given graph H. An (a, d)-H-antimagic labeling of G admitting an H-covering is a bijective function f:V∪E→{1, 2,⋯, |V| + |E|} such that, for all subgraphs H' of G isomorphic to H, the H'-weights, wtf(H') = Σv∈V(H')f(v)+ Σe∈E(H')f(e), constitute an arithmetic progression with the initial term o and the common difference d. Such a labeling is called super if f(V) = {1,2,⋯,|V|}. In this paper, we study the existence of super (a, d)-H-antimagic labelings for graph operation GH, where G is a (super) (b,d∗)-edge-antimagic total graph and H is a connected graph of order at least 3.

Año de publicación:

2017

Keywords:

• H-covering
• (Super) (a,d)-H-antimagic labeling

Fuente:

scopus