Volume 19, Issue No.3

KEY WORDS

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

ABSTRACT

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.

CITATION INFORMATION

Acta Mechanica Slovaca. Volume 19, Issue 3, Pages 6–11, ISSN 1335-2393

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  A Construction of H-antimagic Graphs

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