On irregular total labellings
- Authors: Baca, Martin , Jendrol, Stanislav , Miller, Mirka , Ryan, Joe
- Date: 2007
- Type: Text , Journal article
- Relation: Discrete Mathematics Vol. 307, no. 11-12 (May 2007), p. 1378-1388
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- Description: Two new graph characteristics, the total vertex irregularity strength and the total edge irregularity strength, are introduced. Estimations on these parameters are obtained. For some families of graphs the precise values of these parameters are proved. (c) 2006 Elsevier B.V. All rights reserved.
- Description: C1
- Description: 2003004909
Vertex-magic total labeling of generalized Petersen graphs and convex polytopes
- Authors: Miller, Mirka , Baca, Martin , MacDougall, James
- Date: 2006
- Type: Text , Journal article
- Relation: JCMCC Journal of Combinatorial Mathematics and Combinatorial Computing Vol. 59, no. (2006), p. 89-99
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- Description: To date the study of graph labellings has focused on nding classes of graphs which admit a particular type of labelling. Here we consider variations of the well-known edge-magic and vertex-magic labellings for which all graphs admit such a labelling. In particular we consider two types of labellings of the vertices and edges of a graph with distinct positive integers: (1) for every edge the sum of its label and those of its endvertices is some constant (pseudo edge-magic); and (2) for every vertex the sum of its label and those of the edges incident to it is some constant (pseudo vertex-magic). Our aim is to minimise the constant, called the magic number, associated with the labelling. We present lower and upper bounds on the magic number in pseudo edge-magic and pseudo vertex-magic labellings of complete graphs, trees and arbitrary graphs. In a number of cases these bounds are within a constant factor.
- Description: C1
- Description: 2003001602