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Small regular graphs of girth 7

Author
Abreu, M.; Araujo-Pardo, G.; Balbuena, C.; Labbate, D.; Salas, J.
Type of activity
Journal article
Journal
Electronic journal of combinatorics
Date of publication
2015-07-01
Volume
22
Number
3
First page
1
Last page
16
Repository
http://hdl.handle.net/2117/86686 Open in new window
URL
http://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i3p5 Open in new window
Abstract
In this paper, we construct new infinite families of regular graphs of girth 7 of smallest order known so far. Our constructions are based on combinatorial and geometric properties of (q + 1, 8)-cages, for q a prime power. We remove vertices from such cages and add matchings among the vertices of minimum degree to achieve regularity in the new graphs. We obtain (q + 1)-regular graphs of girth 7 and order 2q(3) + q(2) + 2q for each even prime power q >= 4, and of order 2q(3) + 2q(2) q + 1 for eac...
Citation
Abreu, M., Araujo-Pardo, G., Balbuena, C., Labbate, D., Salas, J. Small regular graphs of girth 7. "Electronic journal of combinatorics", 01 Juliol 2015, vol. 22, núm. 3, p. 1-16.
Keywords
Bipartite graphs, Cages, Construction, Girth, Incidence graph
Group of research
COMBGRAPH - Combinatorics, Graph Theory and Applications

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