1Dipartimento di Matematica, Informatica ed Economia Università degli Studi della Basilicata Viale dell’Ateneo Lucano, I-85100 Potenza, Italy 2Instituto de Matemáticas Universidad Nacional Autónoma de México Ciudad Universitaria, México D.F. 04510, México. 3Departament de Matemàtica Aplicada III Universitat Politècnica de Catalunya Campus Nord, Edifici C2, C/ Jordi Girona 1 i 3 E-08034 Barcelona, Spain. 4Dipartimento di Matematica, Informatica ed Economia Università degli Studi della Basilicata, Viale dell’Ateneo Lucano, I-85100 Potenza, Italy
The electronic journal of combinatorics, Tome 20 (2013) no. 1
Let $2 \le r < m$ and $g$ be positive integers. An $(\{r,m\};g)$-graph (or biregular graph) is a graph with degree set $\{r,m\}$ and girth $g$, and an $(\{r,m\};g)$-cage (or biregular cage) is an $(\{r,m\};g)$-graph of minimum order $n(\{r,m\};g)$. If $m=r+1$, an $(\{r,m\};g)$-cage is said to be a semiregular cage.In this paper we generalize the reduction and graph amalgam operations from [M. Abreu, G. Araujo-Pardo, C. Balbuena, D. Labbate. Families of Small Regular Graphs of Girth $5$. Discrete Math. 312 (2012) 2832--2842] on the incidence graphs of an affine and a biaffine plane obtaining two new infinite families of biregular cages and two new semiregular cages. The constructed new families are $(\{r,2r-3\};5)$-cages for all $r=q+1$ with $q$ a prime power, and $(\{r,2r-5\};5)$-cages for all $r=q+1$ with $q$ a prime. The new semiregular cages are constructed for $r=5$ and $6$ with $31$ and $43$ vertices respectively.
1
Dipartimento di Matematica, Informatica ed Economia
Università degli Studi della Basilicata
Viale dell’Ateneo Lucano, I-85100 Potenza, Italy
2
Instituto de Matemáticas
Universidad Nacional Autónoma de México
Ciudad Universitaria, México D.F. 04510, México.
3
Departament de Matemàtica Aplicada III
Universitat Politècnica de Catalunya
Campus Nord, Edifici C2, C/ Jordi Girona 1 i 3
E-08034 Barcelona, Spain.
4
Dipartimento di Matematica, Informatica ed Economia
Università degli Studi della Basilicata,
Viale dell’Ateneo Lucano, I-85100 Potenza, Italy
@article{10_37236_2594,
author = {Mari\'en Abreu and Gabriela Araujo-Pardo and Camino Balbuena and Domenico Labbate and Gloria L\'opez-Ch\'avez},
title = {Biregular cages of girth five},
journal = {The electronic journal of combinatorics},
year = {2013},
volume = {20},
number = {1},
doi = {10.37236/2594},
zbl = {1266.05072},
url = {http://geodesic.mathdoc.fr/articles/10.37236/2594/}
}
TY - JOUR
AU - Marién Abreu
AU - Gabriela Araujo-Pardo
AU - Camino Balbuena
AU - Domenico Labbate
AU - Gloria López-Chávez
TI - Biregular cages of girth five
JO - The electronic journal of combinatorics
PY - 2013
VL - 20
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/2594/
DO - 10.37236/2594
ID - 10_37236_2594
ER -
