Zobrazeno 1 - 10
of 27
pro vyhledávání: '"Meulen, Kevin N. Vander"'
The Fiedler matrices are a large class of companion matrices that include the well-known Frobenius companion matrix. The Fiedler matrices are part of a larger class of companion matrices that can be characterized with a Hessenberg form. In this paper
Externí odkaz:
http://arxiv.org/abs/2301.13257
The $k$-token graph $T_k(G)$ is the graph whose vertices are the $k$-subsets of vertices of a graph $G$, with two vertices of $T_k(G)$ adjacent if their symmetric difference is an edge of $G$. We explore when $T_k(G)$ is a well-covered graph, that is
Externí odkaz:
http://arxiv.org/abs/2010.04539
It is well-known that the zero forcing number of a graph provides a lower bound on the minimum rank of a graph. In this paper we bound and characterize the zero forcing number of certain circulant graphs, including some bipartite circulants, cubic ci
Externí odkaz:
http://arxiv.org/abs/1906.03079
The Frobenius companion matrix, and more recently the Fiedler companion matrices, have been used to provide lower and upper bounds on the modulus of any root of a polynomial $p(x)$. In this paper we explore new bounds obtained from taking the $1$-nor
Externí odkaz:
http://arxiv.org/abs/1711.02576
Publikováno v:
Linear Algebra and Its Applications 534 (2017) 36-50
We develop a matrix bordering technique that can be applied to an irreducible spectrally arbitrary sign pattern to construct a higher order spectrally arbitrary sign pattern. This technique generalizes a recently developed triangle extension method.
Externí odkaz:
http://arxiv.org/abs/1708.09237
A matrix pattern is often either a sign pattern with entries in {0,+,-} or, more simply, a nonzero pattern with entries in {0,*}. A matrix pattern A is spectrally arbitrary if for any choice of a real matrix spectrum, there is a real matrix having th
Externí odkaz:
http://arxiv.org/abs/1612.03112
We explore how the combinatorial arrangement of prescribed zeros in a matrix affects the possible eigenvalues that the matrix can obtain. We demonstrate that there are inertially arbitrary patterns having a digraph with no 2-cycle, unlike what happen
Externí odkaz:
http://arxiv.org/abs/1611.08217
We focus our attention on well-covered graphs that are vertex decomposable. We show that for many known families of these vertex decomposable graphs, the set of shedding vertices forms a dominating set. We then construct three new infinite families o
Externí odkaz:
http://arxiv.org/abs/1606.04447
We study the independence complexes of families of well-covered circulant graphs discovered by Boros-Gurvich-Milani\v{c}, Brown-Hoshino, and Moussi. Because these graphs are well-covered, their independence complexes are pure simplicial complexes. We
Externí odkaz:
http://arxiv.org/abs/1505.02837
We investigate when the independence complex of $G[H]$, the lexicographical product of two graphs $G$ and $H$, is either vertex decomposable or shellable. As an application, we construct an infinite family of graphs with the property that every graph
Externí odkaz:
http://arxiv.org/abs/1505.02838