Results 21 to 30 of about 1,362 (112)

Hyperbolicity cones of elementary symmetric polynomials are spectrahedral [PDF]

, 2013
We prove that the hyperbolicity cones of elementary symmetric polynomials are spectrahedral, i.e., they are slices of the cone of positive semidefinite matrices.
Brändén, Petter
core   +1 more source

The Arithmetic Tutte polynomial of two matrices associated to Trees

Special Matrices, 2018
Arithmetic matroids arising from a list A of integral vectors in Zn are of recent interest and the arithmetic Tutte polynomial MA(x, y) of A is a fundamental invariant with deep connections to several areas. In this work, we consider two lists of vectors
Bapat R. B., Sivasubramanian Sivaramakrishnan   +1 more
doaj   +1 more source

Steiner distance matrix of caterpillar graphs

Special Matrices, 2022
In this article, we show that the rank of the 2-Steiner distance matrix of a caterpillar graph having NN vertices and pp pendant veritices is 2N−p−12N-p-1.
Azimi Ali, Bapat Ravindra B., Goel Shivani   +2 more
doaj   +1 more source

Diagonalizable matrices whose graph is a tree: the minimum number of distinct eigenvalues and the feasibility of eigenvalue assignments

Special Matrices, 2019
Considered are combinatorially symmetric matrices, whose graph is a given tree, in view of the fact recent analysis shows that the geometric multiplicity theory for the eigenvalues of such matrices closely parallels that for real symmetric (and complex ...
Saiago Carlos M.
doaj   +1 more source

Equating κ Maximum Degrees in Graphs without Short Cycles

Discussiones Mathematicae Graph Theory, 2020
For an integer k at least 2, and a graph G, let fk(G) be the minimum cardinality of a set X of vertices of G such that G − X has either k vertices of maximum degree or order less than k.
Fürst Maximilian, Gentner Michael, Jäger Simon, Rautenbach Dieter, Henning Michael A.   +4 more
doaj   +1 more source

On the number of perfect matchings in random polygonal chains

Open Mathematics, 2023
Let GG be a graph. A perfect matching of GG is a regular spanning subgraph of degree one. Enumeration of perfect matchings of a (molecule) graph is interest in chemistry, physics, and mathematics.
Wei Shouliu, Feng Yongde, Ke Xiaoling, Huang Jianwu   +3 more
doaj   +1 more source

Structures of W(2.2) Lie conformal algebra

Open Mathematics, 2016
The purpose of this paper is to study W(2, 2) Lie conformal algebra, which has a free ℂ[∂]-basis {L, M} such that [LλL]=(∂+2λ)L,[LλM]=(∂+2λ)M,[MλM]=0$\begin{equation}[{L_\lambda }L] = (\partial + 2\lambda )L,[{L_\lambda }M] = (\partial + 2\lambda )M,[{M_\
Yuan Lamei, Wu Henan
doaj   +1 more source

The location of classified edges due to the change in the geometric multiplicity of an eigenvalue in a tree

Special Matrices, 2019
Given a combinatorially symmetric matrix A whose graph is a tree T and its eigenvalues, edges in T can be classified in four categories, based upon the change in geometric multiplicity of a particular eigenvalue, when the edge is removed.
Toyonaga Kenji
doaj   +1 more source

Degree Sum Condition for the Existence of Spanning k-Trees in Star-Free Graphs

Discussiones Mathematicae Graph Theory, 2022
For an integer k ≥ 2, a k-tree T is defined as a tree with maximum degree at most k. If a k-tree T spans a graph G, then T is called a spanning k-tree of G.
Furuya Michitaka, Maezawa Shun-ichi, Matsubara Ryota, Matsuda Haruhide, Tsuchiya Shoichi, Yashima Takamasa   +5 more
doaj   +1 more source

High-Precision Entropy Values for Spanning Trees in Lattices

, 2003
Shrock and Wu have given numerical values for the exponential growth rate of the number of spanning trees in Euclidean lattices. We give a new technique for numerical evaluation that gives much more precise values, together with rigorous bounds on the ...
Ball K, Burton R M, Jessica L Felker, Kirchhoff G, Lyons R, Lyons R, Montroll E, Pemantle R, Russell Lyons, Shrock R, Sokal A D, Spitzer F   +11 more
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