Acta Mechanica Slovaca 2015, 19(3):6-11 | DOI: 10.21496/ams.2015.017

A Construction of H-antimagic Graphs

Mirka Miller¹, Andrea Semaničová-Feňovčíková^2*

¹ School of Mathematical and Physical Sciences, The University of Newcastle, Australia; Department of Mathematics, University of West Bohemia, Pilsen, Czech Republic; Department of Informatics, King's College London, UK

² Department of Applied Mathematics and Informatics, Faculty of Mechanical Engineering, Technical University, Košice, Slovak Republic

Let G = (V,E) be a finite simple graph with p vertices and q edges. An edge-covering of G is a family of subgraphs H1,H2,...,Ht such that each edge of E(G) belongs to at least one of the subgraphs Hi, i=1,2,...,t. If every subgraph Hi is isomorphic to a given graph H, then the graph G admits an H-covering. Such a graph G is called (a,d)-H-antimagic if there is a bijection f: VjEg{1,2,...,p+q} such that for all subgraphs H' of G isomorphic to H, the sum of the labels of all the edges and vertices belonging to H' constitutes an arithmetic progression with the initial term a and the common difference d. When f(V)={1,2,...,p}, then G is said to be super (a,d)-H-antimagic; and if d = 0 then G is called H-supermagic.
We will exhibit an operation on graphs which keeps super H-antimagic properties. We use a technique of partitioning sets of integers for the construction of the required labelings.

Keywords: H-covering, (a,d)-H-antimagic graph, super (a,d)-H-antimagic graph, partition of set

Published: October 31, 2015  Show citation