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View article: On Bipartite Biregular Large Graphs Derived From Difference Sets
On Bipartite Biregular Large Graphs Derived From Difference Sets Open
A bipartite graph with is biregular if all the vertices of each stable set, and , have the same degree, and , respectively. This paper studies difference sets derived from both Abelian and non‐Abelian groups. From them, we propose some con…
View article: Bounds in radial Moore graphs of diameter 3
Bounds in radial Moore graphs of diameter 3 Open
Radial Moore graphs are approximations of Moore graphs that preserve the distance-preserving spanning tree for its central vertices. One way to classify their resemblance with a Moore graph is the status measure. The status of a graph is d…
View article: On bipartite biregular large graphs
On bipartite biregular large graphs Open
A bipartite graph $G=(V,E)$ with $V=V_1\cup V_2$ is biregular if all the vertices of each stable set, $V_1$ and $V_2$, have the same degree, $r$ and $s$, respectively. This paper studies difference sets derived from both Abelian and non-Ab…
View article: On large regular (1,1,k)-mixed graphs
On large regular (1,1,k)-mixed graphs Open
An $(r,z,k)$-mixed graph $G$ has every vertex with undirected degree $r$, directed in- and out-degree $z$, and diameter $k$. In this paper, we study the case $r=z=1$, proposing some new constructions of $(1,1,k)$-mixed graphs with a large …
View article: Nonexistence of Almost Moore Digraphs of Degrees 4 and 5 with Self-Repeats
Nonexistence of Almost Moore Digraphs of Degrees 4 and 5 with Self-Repeats Open
An almost Moore $(d,k)$-digraph is a regular digraph of degree $d>1$, diameter $k>1$ and order $N(d,k)=d+d^2+\cdots +d^k$. So far, their existence has only been shown for $k=2$, whilst it is known that there are no such digraphs for $k=3$,…
View article: On mixed radial Moore graphs of diameter 3
On mixed radial Moore graphs of diameter 3 Open
Radial Moore graphs and digraphs are extremal graphs related to the Moore ones where the distance-preserving spanning tree is preserved for some vertices. This leads to classify them according to their proximity to being a Moore graph or d…
View article: Almost Moore and the largest mixed graphs of diameters two and three
Almost Moore and the largest mixed graphs of diameters two and three Open
Almost Moore mixed graphs\/} appear in the context of the degree/diameter problem as a class of extremal mixed graphs, in the sense that their order is one unit less than the Moore bound for such graphs. The problem of their existence has …
View article: The Contemporary project : avant-garde-post-avant-garde attitude : 8th edition
The Contemporary project : avant-garde-post-avant-garde attitude : 8th edition Open
"Organized by: Cercle d’Arquitectura Research Group, Departament de Projectes Arquitectònics, Escola Tècnica Superior d’Arquitectura de Barcelona, Universitat Politècnica de Catalunya" -- Coberta
View article: Graph Theory-Based Characterization and Classification of Household Photovoltaics
Graph Theory-Based Characterization and Classification of Household Photovoltaics Open
With the clear goal of improving photovoltaic (PV) technology performance towards nearly-zero energy buildings, a graph theory-based model that characterizes photovoltaic panel structures is developed. An algorithm to obtain all possible c…
View article: New results for the Mondrian art problem
New results for the Mondrian art problem Open
© 2021 Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
View article: Decompositions of a rectangle into non-congruent rectangles of equal area
Decompositions of a rectangle into non-congruent rectangles of equal area Open
In this paper, we deal with a simple geometric problem: Is it possible to partition a rectangle into $k$ non-congruent rectangles of equal area? This problem is motivated by the so-called `Mondrian art problem' that asks a similar question…
View article: New results for the Mondrian art problem
New results for the Mondrian art problem Open
The Mondrian problem consists of dissecting a square of side length $n\in \NN$ into non-congruent rectangles with natural length sides such that the difference $d(n)$ between the largest and the smallest areas of the rectangles partitionin…
View article: An improved Moore bound and some new optimal families of mixed Abelian Cayley graphs
An improved Moore bound and some new optimal families of mixed Abelian Cayley graphs Open
We consider the case in which mixed graphs (with both directed and undirected edges) are Cayley graphs of Abelian groups. In this case, some Moore bounds were derived for the maximum number of vertices that such graphs can attain. We first…
View article: New Moore-Like Bounds and Some Optimal Families of Abelian Cayley Mixed Graphs
New Moore-Like Bounds and Some Optimal Families of Abelian Cayley Mixed Graphs Open
The final publication is available at Springer via http://dx.doi.org/10.1007/s00026-020-00496-2
View article: On new record graphs close to bipartite Moore graphs
On new record graphs close to bipartite Moore graphs Open
The modelling of interconnection networks by graphs motivated the study of several extremal problems that involve well known parameters of a graph (degree, diameter, girth and order) and ask for the optimal value of one of them while holdi…
View article: PageRank regular digraphs with prime out-degrees
PageRank regular digraphs with prime out-degrees Open
The PageRank algorithm was designed to rank web pages according to their relevance in the web. In this context, web topology is modeled as a directed graph whose vertices correspond to web pages wi...
View article: New results on the degree/diameter problem of mixed Abelian Cayley graphs
New results on the degree/diameter problem of mixed Abelian Cayley graphs Open
Mixed graphs can be seen as digraphs that have both arcs and edges (or digons, that is, two opposite arcs). In this paper, we consider the case in which such graphs are Cayley graphs of Abelian groups. These groups can be constructed by us…
View article: On bipartite‐mixed graphs
On bipartite‐mixed graphs Open
Mixed graphs can be seen as digraphs that have both arcs and edges (or digons, that is, two opposite arcs). In this article, we consider the case where such graphs are bipartite. As main results, we show that in this context the Moore‐like…
View article: The Degree/Diameter Problem for mixed abelian Cayley graphs
The Degree/Diameter Problem for mixed abelian Cayley graphs Open
This paper investigates the upper bounds for the number of vertices in mixed abelian Cayley graphs with given degree and diameter. Additionally, in the case when the undirected degree is equal to one, we give a construction that provides a…