arXiv subjects

Araujo-Pardo Gabriela

Publications and source records attributed to Araujo-Pardo Gabriela.

2 recordsLinked to original sources

arXiv2026

On balanced biregular cages

In this paper, we introduce a problem closely related to the {\emph{Cage Problem}}. We are interested in {\emph{Balanced Biregular Cages}}, which are the smallest biregular graphs of fixed girth that have the same number of vertices of one degree as the other. We introduce the graphs and obtain lower and upper bounds for some values of degree and girth. In particular, we construct relatively small balanced biregular graphs from incidence graphs of finite projective, affine, and biaffine planes and we show that some of the obtained graphs are balanced biregular cages.

math.CO↗

arXiv2021

Edge-girth-regular graphs arising from biaffine planes and Suzuki groups

An edge-girth-regular graph $egr(v,k,g,λ)$, is a $k$-regular graph of order $v$, girth $g$ and with the property that each of its edges is contained in exactly $λ$ distinct $g$-cycles. An $egr(v,k,g,λ)$ is called extremal for the triple $(k,g,λ)$ if $v$ is the smallest order of any $egr(v,k,g,λ)$. In this paper, we introduce two families of edge-girth-regular graphs. The first one is a family of extremal $egr(2q^2,q,6,(q-1)^2(q-2))$ for any prime power $q\geq 3$ and, the second one is a family of $egr(q(q^2+1),q,5,λ)$ for $λ\geq q-1$ and $q\geq 8$ an odd power of $2$. In particular, if $q=8$ we have that $λ=q-1$.

math.CO↗