All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 23 Next

Displaying 441 – 460 of 498

Showing per page

The Laplacian spectrum of some digraphs obtained from the wheel

Li Su, Hong-Hai Li, Liu-Rong Zheng (2012)

Discussiones Mathematicae Graph Theory

The problem of distinguishing, in terms of graph topology, digraphs with real and partially non-real Laplacian spectra is important for applications. Motivated by the question posed in [R. Agaev, P. Chebotarev, Which digraphs with rings structure are essentially cyclic?, Adv. in Appl. Math. 45 (2010), 232-251], in this paper we completely list the Laplacian eigenvalues of some digraphs obtained from the wheel digraph by deleting some arcs.

The Laplacian spread of graphs

Zhifu You, Bo Lian Liu (2012)

Czechoslovak Mathematical Journal

The Laplacian spread of a graph is defined as the difference between the largest and second smallest eigenvalues of the Laplacian matrix of the graph. In this paper, bounds are obtained for the Laplacian spread of graphs. By the Laplacian spread, several upper bounds of the Nordhaus-Gaddum type of Laplacian eigenvalues are improved. Some operations on Laplacian spread are presented. Connected c -cyclic graphs with n vertices and Laplacian spread n - 1 are discussed.

The Least Eigenvalue of Graphs whose Complements Are Uni- cyclic

Yi Wang, Yi-Zheng Fan, Xiao-Xin Li, Fei-Fei Zhang (2015)

Discussiones Mathematicae Graph Theory

A graph in a certain graph class is called minimizing if the least eigenvalue of its adjacency matrix attains the minimum among all graphs in that class. Bell et al. have identified a subclass within the connected graphs of order n and size m in which minimizing graphs belong (the complements of such graphs are either disconnected or contain a clique of size n/2 ). In this paper we discuss the minimizing graphs of a special class of graphs of order n whose complements are connected and contains...

The maximum multiplicity and the two largest multiplicities of eigenvalues in a Hermitian matrix whose graph is a tree

Rosário Fernandes (2015)

Special Matrices

The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree, M1, was understood fully (froma combinatorial perspective) by C.R. Johnson, A. Leal-Duarte (Linear Algebra and Multilinear Algebra 46 (1999) 139-144). Among the possible multiplicity lists for the eigenvalues of Hermitian matrices whose graph is a tree, we focus upon M2, the maximum value of the sum of the two largest multiplicities when the largest multiplicity is M1. Upper and lower bounds are given for M2. Using a combinatorial...

The Minimum Spectral Radius of Signless Laplacian of Graphs with a Given Clique Number

Li Su, Hong-Hai Li, Jing Zhang (2014)

Discussiones Mathematicae Graph Theory

In this paper we observe that the minimal signless Laplacian spectral radius is obtained uniquely at the kite graph PKn−ω,ω among all connected graphs with n vertices and clique number ω. In addition, we show that the spectral radius μ of PKm,ω (m ≥ 1) satisfies [...] More precisely, for m > 1, μ satisfies the equation [...] where [...] and [...] . At last the spectral radius μ(PK∞,ω) of the infinite graph PK∞,ω is also discussed.

The real symmetric matrices of odd order with a P-set of maximum size

Zhibin Du, Carlos M. da Fonseca (2016)

Czechoslovak Mathematical Journal

Suppose that A is a real symmetric matrix of order n . Denote by m A ( 0 ) the nullity of A . For a nonempty subset α of { 1 , 2 , ... , n } , let A ( α ) be the principal submatrix of A obtained from A by deleting the rows and columns indexed by α . When m A ( α ) ( 0 ) = m A ( 0 ) + | α | , we call α a P-set of A . It is known that every P-set of A contains at most ⌊ n / 2 ⌋ elements. The graphs of even order for which one can find a matrix attaining this bound are now completely characterized. However, the odd case turned out to be more difficult to tackle. As a first step...

The Wigner semi-circle law and the Heisenberg group

Jacques Faraut, Linda Saal (2007)

Banach Center Publications

The Wigner Theorem states that the statistical distribution of the eigenvalues of a random Hermitian matrix converges to the semi-circular law as the dimension goes to infinity. It is possible to establish this result by using harmonic analysis on the Heisenberg group. In fact this convergence corresponds to the topology of the set of spherical functions associated to the action of the unitary group on the Heisenberg group.

Currently displaying 441 – 460 of 498