Note: A note on the upper bound and girth pair of (k;g)-cages

Authors:
C. Balbuena;D. GonzáLez-Moreno;J. J. Montellano-Ballesteros
Affiliations:
Departament de Matemítica Aplicada III, Universitat Politècnica de Catalunya, Spain;Departamento de Matemáticas Aplicadas y Sistemas, Universidad Autónoma Metropolitana - Cuajimalpa, Mexico;Instituto de Matemáticas, Universidad Nacional Autónoma de México, Mexico
Venue:
Discrete Applied Mathematics
Year:
2013

Citing 3
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Connectivity of cages

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Some remarks on the Kronecker product of graphs

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A lower bound on the order of regular graphs with given girth pair

Journal of Graph Theory

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Abstract

A (k;g)-cage is a k-regular graph of girth g with minimum order. In this work, for all k=3 and g=5 odd, we present an upper bound of the order of a (k;g+1)-cage in terms of the order of a (k;g)-cage, improving a previous result by Sauer of 1967. We also show that every (k;11)-cage with k=6 contains a cycle of length 12, supporting a conjecture by Harary and Kovacs of 1983.