- 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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