Vertex Antimagic Total Labeling of Digraphs

• Journal title : Kyungpook mathematical journal
• Volume 55, Issue 2,  2015, pp.267-277
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2015.55.2.267
Title & Authors
Vertex Antimagic Total Labeling of Digraphs

Abstract
In this paper we investigate the properties of (a, d)-vertex antimagic total labeling of a digraph D = (V, A). In this labeling, we assign to the vertices and arcs the consecutive integers from 1 to |V|+|A| and calculate the sum of labels at each vertex, i.e., the vertex label added to the labels on its out arcs. These sums form an arithmetical progression with initial term a and common difference d. We show the existence and non-existence of (a, d)-vertex antimagic total labeling for several class of digraphs, and show how to construct labelings for generalized de Bruijn digraphs. We conclude this paper with an open problem suitable for further research.
Keywords
(a, d)-vertex antimagic labeling;Generalized de Bruijn digraphs;
Language
English
Cited by
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