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On bi-regular cages of even girth at least 8

Author
Araujo-Pardo, G.; Balbuena, C.; Lopez -Chavez, G.; Montejano, L.
Type of activity
Journal article
Journal
Aequationes mathematicae
Date of publication
2013-12
Volume
86
Number
3
First page
201
Last page
216
DOI
https://doi.org/10.1007/s00010-013-0227-5 Open in new window
Project funding
Control de invariantes en grafos sujetos a propiedades estructurales
Abstract
Let r, m, 2 = r < m and g = 3 be three positive integers. A graph with a prescribed degree set r, m and girth g having the least possible number of vertices is called a bi-regular cage or an (r, m; g)-cage, and its order is denoted by n(r, m; g). In this paper we provide upper bounds on n(r, m; g) for some related values of r, m and even girth g at least 8. Moreover, if r - 1 is a prime power and m = 5, we construct the smallest currently known (r, m; 8)-graphs. Also, if r = 3 and m = 7 is not d...
Keywords
Bi-regular, cage, girth
Group of research
COMBGRAPH - Combinatorics, Graph Theory and Applications

Participants