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Displaying 341 – 360 of 540

On the spectral radius of $‡$ -shape trees

Xiaoling Ma, Fei Wen (2013)

Czechoslovak Mathematical Journal

Let $A (G)$ be the adjacency matrix of $G$ . The characteristic polynomial of the adjacency matrix $A$ is called the characteristic polynomial of the graph $G$ and is denoted by $φ (G, λ)$ or simply $φ (G)$ . The spectrum of $G$ consists of the roots (together with their multiplicities) $λ_{1} (G) \geq λ_{2} (G) \geq ... \geq λ_{n} (G)$ of the equation $φ (G, λ) = 0$ . The largest root $λ_{1} (G)$ is referred to as the spectral radius of $G$ . A $‡$ -shape is a tree with exactly two of its vertices having maximal degree 4. We will denote by $G (l_{1}, l_{2}, ..., l_{7})$ $...$

On the spectrum of the derangement graph.

Renteln, Paul (2007) The Electronic Journal of Combinatorics [electronic only]

On the strong Arnol'd hypothesis and the connectivity of graphs.

Van Der Holst, Hein (2010) ELA. The Electronic Journal of Linear Algebra [electronic only]

On the structure of path-like trees

F.A. Muntaner-Batle, Miquel Rius-Font (2008) Discussiones Mathematicae Graph Theory

We study the structure of path-like trees. In order to do this, we introduce a set of trees that we call expandable trees. In this paper we also generalize the concept of path-like trees and we call such generalization generalized path-like trees. As in the case of path-like trees, generalized path-like trees, have very nice labeling properties.

On the sum of powers of Laplacian eigenvalues of bipartite graphs

Bo Zhou, Aleksandar Ilić (2010) Czechoslovak Mathematical Journal

For a bipartite graph

G

and a non-zero real

α

, we give bounds for the sum of the

α

th powers of the Laplacian eigenvalues of

G

using the sum of the squares of degrees, from which lower and upper bounds for the incidence energy, and lower bounds for the Kirchhoff index and the Laplacian Estrada index are deduced.

On the Symbolic Evaluation of Determinants

Christos H. Papadimitriou (1980)

Δελτίο της Ελληνικής Μαθηματικής Εταιρίας

On two conjectures regarding an inverse eigenvalue problem for acyclic symmetric matrices.

Barioli, Franceso, Fallat, Shaun M. (2004)

ELA. The Electronic Journal of Linear Algebra [electronic only]

On $λ_{1}$ -extremal non-regular graphs.

Liu, Bolian, Huang, Yufei, You, Zhifu (2009)

ELA. The Electronic Journal of Linear Algebra [electronic only]

Order unicyclic graphs according to spectral radius of unoriented laplacian matrix

Yi-Zheng Fan, Song Wu (2008)

Discussiones Mathematicae Graph Theory

The spectral radius of a graph is defined by that of its unoriented Laplacian matrix. In this paper, we determine the unicyclic graphs respectively with the third and the fourth largest spectral radius among all unicyclic graphs of given order.

Ordering Cacti With $n$ Vertices and $k$ Cycles by Their Laplacian Spectral Radii

Shu-Guang Guo, Yan-Feng Wang (2012)

Publications de l'Institut Mathématique

Ordering unicyclic graphs in terms of their smaller least eigenvalues.

Xu, Guang-Hui (2010)

Journal of Inequalities and Applications [electronic only]

Packing independent sets and transversals

D. de-Werra (1989)

Banach Center Publications

Partial sum of eigenvalues of random graphs

Israel Rocha (2020)

Applications of Mathematics

Let $G$ be a graph on $n$ vertices and let $λ_{1} \geq λ_{2} \geq ... \geq λ_{n}$ be the eigenvalues of its adjacency matrix. For random graphs we investigate the sum of eigenvalues $s_{k} = \sum_{i = 1}^{k} λ_{i}$ , for $1 \leq k \leq n$ , and show that a typical graph has $s_{k} \leq (e (G) + k^{2}) / {(0.99 n)}^{1 / 2}$ , where $e (G)$ is the number of edges of $G$ . We also show bounds for the sum of eigenvalues within a given range in terms of the number of edges. The approach for the proofs was first used in Rocha (2020) to bound the partial sum of eigenvalues of the Laplacian matrix.

Pentadiagonal Companion Matrices

Brydon Eastman, Kevin N. Vander Meulen (2016)

Special Matrices

The class of sparse companion matrices was recently characterized in terms of unit Hessenberg matrices. We determine which sparse companion matrices have the lowest bandwidth, that is, we characterize which sparse companion matrices are permutationally similar to a pentadiagonal matrix and describe how to find the permutation involved. In the process, we determine which of the Fiedler companion matrices are permutationally similar to a pentadiagonal matrix. We also describe how to find a Fiedler...