43 research outputs found
A Study of Arc Strong Connectivity of Digraphs
My dissertation research was motivated by Matula and his study of a quantity he called the strength of a graph G, kappa\u27( G) = max{lcub}kappa\u27(H) : H G{rcub}. (Abstract shortened by ProQuest.)
Minimal strong digraphs
We introduce adequate concepts of expansion of a digraph to obtain a sequential construction of minimal strong digraphs. We obtain a characterization of the class of minimal strong digraphs whose expansion preserves the property of minimality. We prove that every minimal strong digraph of order nmayor que=2 is the expansion of a minimal strong digraph of order n-1 and we give sequentially generative procedures for the constructive characterization of the classes of minimal strong digraphs. Finally we describe algorithms to compute unlabeled minimal strong digraphs and their isospectral classes
Structural properties of minimal strong digraphs versus trees
Producción CientíficaIn this article, we focus on structural properties of minimal strong digraphs
(MSDs). We carry out a comparative study of properties of MSDs versus (undirected) trees. For some of these properties, we give the matrix version, regarding
nearly reducible matrices. We give bounds for the coefficients of the characteristic polynomial corresponding to the adjacency matrix of trees, and we conjecture
bounds for MSDs. We also propose two different representations of an MSD in
terms of trees (the union of a spanning tree and a directed forest; and a double
directed tree whose vertices are given by the contraction of connected Hasse
diagrams).Ministerio de Economía, Industria y Competitividad ( grant MTM2015-65764-C3-1-P
Maximum size of -free strong digraphs with out-degree at least two
Let be a family of digraphs. A digraph is
\emph{-free} if it contains no isomorphic copy of any member of
. For , we set ,
where is a directed cycle of length . Let
denote the family of \emph{-free} strong
digraphs on vertices with every vertex having out-degree at least and
in-degree at least , where both and are positive integers.
Let and
. Bermond et al.\;(1980) verified that
. Chen and Chang\;(2021) showed that
. This upper bound
was further improved to by Chen and Chang\;(DAM, 2022),
furthermore, they also gave the exact values of for
. In this paper, we continue to determine the exact values of
for , i.e.,
for .Comment: 21 page
Functional Integration of Ecological Networks through Pathway Proliferation
Large-scale structural patterns commonly occur in network models of complex
systems including a skewed node degree distribution and small-world topology.
These patterns suggest common organizational constraints and similar functional
consequences. Here, we investigate a structural pattern termed pathway
proliferation. Previous research enumerating pathways that link species
determined that as pathway length increases, the number of pathways tends to
increase without bound. We hypothesize that this pathway proliferation
influences the flow of energy, matter, and information in ecosystems. In this
paper, we clarify the pathway proliferation concept, introduce a measure of the
node--node proliferation rate, describe factors influencing the rate, and
characterize it in 17 large empirical food-webs. During this investigation, we
uncovered a modular organization within these systems. Over half of the
food-webs were composed of one or more subgroups that were strongly connected
internally, but weakly connected to the rest of the system. Further, these
modules had distinct proliferation rates. We conclude that pathway
proliferation in ecological networks reveals subgroups of species that will be
functionally integrated through cyclic indirect effects.Comment: 29 pages, 2 figures, 3 tables, Submitted to Journal of Theoretical
Biolog