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, wt<inf>f</inf>(H') = Σ<inf>v∈V(H')</inf>f(v)+ Σ<inf>e∈E(H')</inf>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 G^H, 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