Consecutive magic graphs

Title: Consecutive magic graphs
Creator: Balbuena, Camino; Barker, Ewan; Lin, Yuqing; Miller, Mirka; Sugeng, Kiki Ariyanti
Date: 2006
Type: Text; Journal article
Identifier: http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/37151
Identifier: vital:93
Identifier: https://doi.org/10.1016/j.disc.2006.03.064
Identifier: ISSN:0012-365X
Abstract: Let G be a graph of order n and size e. A vertex-magic total labeling is an assignment of the integers 1, 2, ..., n + e to the vertices and the edges of G, so that at each vertex, the vertex label and the labels on the edges incident at that vertex, add to a fixed constant, called the magic number of G. Such a labeling is a-vertex consecutive magic if the set of the labels of the vertices is { a + 1, a + 2, ..., a + n }, and is b-edge consecutive magic if the set of labels of the edges is { b + 1, b + 2, ..., b + e }. In this paper we prove that if an a-vertex consecutive magic graph has isolated vertices then the order and the size satisfy (n - 1); C1
Publisher: Elsevier
Relation: Discrete Mathematics Vol. 306, no. 16 (2006), p. 1817-1829
Rights: Copyright Elsevier
Rights: This metadata is freely available under a CCO license
Subject: 0101 Pure Mathematics; Consecutive magic labeling; Super vertex-magic labeling; Vertex-magic labeling; Computation theory; Number theory; Optimisation; Theorem proving; Isolated vertices; Graph theory
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