arXiv subjects

Hebert Perez-Roses

Publications and source records attributed to Hebert Perez-Roses.

2 recordsLinked to original sources

arXiv2015

Searching for Large Circulant Graphs

We address the problem of constructing large undirected circulant networks with given degree and diameter. First we discuss the theoretical upper bounds and their asymptotics, and then we describe and implement a computer-based method to find large circulant graphs with given parameters. For several combinations of degree and diameter, our algorithm produces the largest known circulant graphs. We summarize our findings in a table, up to degree 15 and diameter 10, and we perform a statistical analysis of this table, which can be useful for evaluating the performance of our methods, as well as other constructions in the future.

math.CO↗

arXiv2012

The Maximum Degree-and-Diameter-Bounded Subgraph in the Mesh

The problem of finding the largest connected subgraph of a given undirected host graph, subject to constraints on the maximum degree $\Delta$ and the diameter $D$, was introduced in \cite{maxddbs}, as a generalization of the Degree-Diameter Problem. A case of special interest is when the host graph is a common parallel architecture. Here we discuss the case when the host graph is a $k$-dimensional mesh. We provide some general bounds for the order of the largest subgraph in arbitrary dimension $k$, and for the particular cases of $k=3, \Delta = 4$ and $k=2, \Delta = 3$, we give constructions that result in sharper lower bounds.

math.CO↗