Zobrazeno 1 - 10
of 501
pro vyhledávání: '"Balbuena, C."'
Given an integer $\ell\ge 1$, a $(1,\le \ell)$-identifying code in a digraph is a dominating subset $C$ of vertices such that all distinct subsets of vertices of cardinality at most $\ell$ have distinct closed in-neighbourhood within $C$. In this pap
Externí odkaz:
http://arxiv.org/abs/1905.05083
A $(1,\le \ell)$-identifying code in a digraph $D$ is a subset $C$ of vertices of $D$ such that all distinct subsets of vertices of cardinality at most $\ell$ have different closed in-neighborhoods within $C$. In this paper, we give some sufficient c
Externí odkaz:
http://arxiv.org/abs/1902.04913
Autor:
Balbuena, C., Frechero, M.A.
Publikováno v:
In Computational Materials Science December 2022 215
In this paper we are interested in the {\it{Cage Problem}} that consists in constructing regular graphs of given girth $g$ and minimum order. We focus on girth $g=5$, where cages are known only for degrees $k \le 7$. We construct regular graphs of gi
Externí odkaz:
http://arxiv.org/abs/1508.01569
In this note we construct a new infinite family of $(q-1)$-regular graphs of girth $8$ and order $2q(q-1)^2$ for all prime powers $q\ge 16$, which are the smallest known so far whenever $q-1$ is not a prime power or a prime power plus one itself.
Externí odkaz:
http://arxiv.org/abs/1501.02452
Let $q\ge 2$ be a prime power. In this note we present a formulation for obtaining the known $(q+1,8)$-cages which has allowed us to construct small $(k,g)$--graphs for $k=q-1, q$ and $g=7,8$. Furthermore, we also obtain smaller $(q,8)$-graphs for ev
Externí odkaz:
http://arxiv.org/abs/1501.02448
Publikováno v:
In Applied Mathematics and Computation 15 October 2020 383
Publikováno v:
In Linear Algebra and Its Applications 1 June 2019 570:138-147
The first known families of cages arised from the incidence graphs of generalized polygons of order $q$, $q$ a prime power. In particular, $(q+1,6)$--cages have been obtained from the projective planes of order $q$. Morever, infinite families of smal
Externí odkaz:
http://arxiv.org/abs/1211.2672
Publikováno v:
Electron. J. Combin. 20(1) (2013) #P71, 1--14
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
Externí odkaz:
http://arxiv.org/abs/1211.0910