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Displaying 121 – 140 of 546

Disconnected vertex sets and equidistant code pairs.

Haemers, Willem H. (1997)

The Electronic Journal of Combinatorics [electronic only]

Discrepancy and eigenvalues of Cayley graphs

Yoshiharu Kohayakawa, Vojtěch Rödl, Mathias Schacht (2016)

Czechoslovak Mathematical Journal

We consider quasirandom properties for Cayley graphs of finite abelian groups. We show that having uniform edge-distribution (i.e., small discrepancy) and having large eigenvalue gap are equivalent properties for such Cayley graphs, even if they are sparse. This affirmatively answers a question of Chung and Graham (2002) for the particular case of Cayley graphs of abelian groups, while in general the answer is negative.

Disjoint unions of complete graphs characterized by their Laplacian spectrum.

Boulet, Romain (2009)

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

Distance matrices perturbed by Laplacians

Balaji Ramamurthy, Ravindra Bhalchandra Bapat, Shivani Goel (2020)

Applications of Mathematics

Let $T$ be a tree with $n$ vertices. To each edge of $T$ we assign a weight which is a positive definite matrix of some fixed order, say, $s$ . Let $D_{i j}$ denote the sum of all the weights lying in the path connecting the vertices $i$ and $j$ of $T$ . We now say that $D_{i j}$ is the distance between $i$ and $j$ . Define $D : = [D_{i j}]$ , where $D_{i i}$ is the $s \times s$ null matrix and for $i \neq j$ , $D_{i j}$ is the distance between $i$ and $j$ . Let $G$ be an arbitrary connected weighted graph with $n$ vertices, where each weight is a positive definite matrix of order $s$ . If $i$ and...

Distances on the tropical line determined by two points

María Jesús de la Puente (2014)

Kybernetika

Let $p^{'}$ and $q^{'}$ be points in $ℝ^{n}$ . Write $p^{'} \sim q^{'}$ if $p^{'} - q^{'}$ is a multiple of $(1, ..., 1)$ . Two different points $p$ and $q$ in $ℝ^{n} / \sim$ uniquely determine a tropical line $L (p, q)$ passing through them and stable under small perturbations. This line is a balanced unrooted semi-labeled tree on $n$ leaves. It is also a metric graph. If some representatives $p^{'}$ and $q^{'}$ of $p$ and $q$ are the first and second columns of some real normal idempotent order $n$ matrix $A$ , we prove that the tree $L (p, q)$ is described by a matrix $F$ , easily obtained from $A$ . We also prove that...

Dominating properties of star complements.

Liu, Bolian, Rowlinson, Peter (2000)

Publications de l'Institut Mathématique. Nouvelle Série

Eigenvalue bounds for some classes of matrices associated with graphs

Ranjit Mehatari, M. Rajesh Kannan (2021)

Czechoslovak Mathematical Journal

For a given complex square matrix $A$ with constant row sum, we establish two new eigenvalue inclusion sets. Using these bounds, first, we derive bounds for the second largest and the smallest eigenvalues of adjacency matrices of $k$ -regular graphs. Then we establish some bounds for the second largest and the smallest eigenvalues of the normalized adjacency matrices of graphs and the second smallest and the largest eigenvalues of the Laplacian matrices of graphs. The sharpness of these bounds is verified...

Eigenvalue Bounds for the Signless Laplacian

Dragoš Cvetković, Peter Rowlinson, Slobodan Simić (2007)

Publications de l'Institut Mathématique

Eigenvalue Conditions for Induced Subgraphs

Jochen Harant, Julia Niebling, Sebastian Richter (2015)

Discussiones Mathematicae Graph Theory

Necessary conditions for an undirected graph G to contain a graph H as induced subgraph involving the smallest ordinary or the largest normalized Laplacian eigenvalue of G are presented.

In this paper equienergetic self-complementary graphs on $p$ vertices for every $p = 4 k$ , $k \geq 2$ and $p = 24 t + 1$ , $t \geq 3$ are constructed.

Currently displaying 121 – 140 of 546

Previous Page 7 Next

Displaying 121 – 140 of 546

Disconnected vertex sets and equidistant code pairs.

Discrepancy and eigenvalues of Cayley graphs

Disjoint unions of complete graphs characterized by their Laplacian spectrum.

Distance matrices perturbed by Laplacians

Distances on the tropical line determined by two points

Dominating properties of star complements.

Eigenvalue bounds for some classes of matrices associated with graphs

Eigenvalue Bounds for the Signless Laplacian

Eigenvalue Conditions for Induced Subgraphs

Eigenvalues and domination in graphs

Eigenvalues and the max-cut problem

Eigenvalues and weights of induced subgraphs.

Eigenvectors and reconstruction.

Equienergetic graphs

Equienergetic self-complementary graphs

Erratum to “A note on the largest eigenvalue of non-regular graphs”.

Estimation of the index of $G^{2}$

Estimation of the maximum multiplicity of an eigenvalue in terms of the vertex degrees of the graph of a matrix.

Estrada index of iterated line graphs

Even and odd tournament matrices with minimum rank over finite fields.

Currently displaying 121 – 140 of 546