13 research outputs found
Maximal independent sets and maximal matchings in series-parallel and related graph classes
The goal of this paper is to obtain quantitative results on the number and on the size of maximal independent sets and maximal matchings in several block-stable graph classes that satisfy a proper sub-criticality condition. In particular we cover trees, cacti graphs and seriesparallel graphs. The proof methods are based on a generating function approach and a proper singularity analysis of solutions of implicit systems of functional equations in several variables. As a byproduct, this method extends previous results of Meir and Moon for trees [Meir, Moon: On maximal independent sets of nodes in trees, Journal of Graph Theory 1988].Postprint (author's final draft
On Maximal Distance Energy
Let G be a graph of order n. If the maximal connected subgraph of G has no cut vertex then it is called a block. If each block of graph G is a clique then G is called clique tree. The distance energy ED(G) of graph G is the sum of the absolute values of the eigenvalues of the distance matrix D(G). In this paper, we study the properties on the eigencomponents corresponding to the distance spectral radius of some special class of clique trees. Using this result we characterize a graph which gives the maximum distance spectral radius among all clique trees of order n with k cliques. From this result, we confirm a conjecture on the maximum distance energy, which was given in Lin et al. Linear Algebra Appl 467(2015) 29-39
Sombor index – one year later
The Sombor index (SO) is a vertex–degree–based graph invariant, invented
in the Summer of 2020, and made publicly available in early 2021. In less than one year, a
remarkable number (almost fifty) research papers on this topological index were produced.
In the present article, we summarize the results achieved so far, and offer a few more.Bulletin t. 153 de l'Académie serbe des sciences et des arts. Classe des sciences mathématiques et naturelles. Sciences mathematiques no 45
Towards Data-Driven Large Scale Scientific Visualization and Exploration
Technological advances have enabled us to acquire extremely large
datasets but it remains a challenge to store, process, and extract
information from them. This dissertation builds upon recent advances
in machine learning, visualization, and user interactions to
facilitate exploration of large-scale scientific datasets. First, we
use data-driven approaches to computationally identify regions of
interest in the datasets. Second, we use visual presentation for
effective user comprehension. Third, we provide interactions for
human users to integrate domain knowledge and semantic information
into this exploration process.
Our research shows how to extract, visualize, and explore informative
regions on very large 2D landscape images, 3D volumetric datasets,
high-dimensional volumetric mouse brain datasets with thousands of
spatially-mapped gene expression profiles, and geospatial trajectories
that evolve over time. The contribution of this dissertation include:
(1) We introduce a sliding-window saliency model that discovers
regions of user interest in very large images; (2) We develop visual
segmentation of intensity-gradient histograms to identify meaningful
components from volumetric datasets; (3) We extract boundary surfaces
from a wealth of volumetric gene expression mouse brain profiles to
personalize the reference brain atlas; (4) We show how to efficiently
cluster geospatial trajectories by mapping each sequence of locations
to a high-dimensional point with the kernel distance framework.
We aim to discover patterns, relationships, and anomalies that would
lead to new scientific, engineering, and medical advances. This work
represents one of the first steps toward better visual understanding
of large-scale scientific data by combining machine learning and human
intelligence
Discrete Mathematics and Symmetry
Some of the most beautiful studies in Mathematics are related to Symmetry and Geometry. For this reason, we select here some contributions about such aspects and Discrete Geometry. As we know, Symmetry in a system means invariance of its elements under conditions of transformations. When we consider network structures, symmetry means invariance of adjacency of nodes under the permutations of node set. The graph isomorphism is an equivalence relation on the set of graphs. Therefore, it partitions the class of all graphs into equivalence classes. The underlying idea of isomorphism is that some objects have the same structure if we omit the individual character of their components. A set of graphs isomorphic to each other is denominated as an isomorphism class of graphs. The automorphism of a graph will be an isomorphism from G onto itself. The family of all automorphisms of a graph G is a permutation group
Collection of abstracts of the 24th European Workshop on Computational Geometry
International audienceThe 24th European Workshop on Computational Geomety (EuroCG'08) was held at INRIA Nancy - Grand Est & LORIA on March 18-20, 2008. The present collection of abstracts contains the 63 scientific contributions as well as three invited talks presented at the workshop