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Let $G$ be a connected graph with vertex set $V (G) = {v_{1}, v_{2}, ..., v_{n}}$ . The distance matrix $D (G) = {(d_{i j})}_{n \times n}$ is the matrix indexed by the vertices of $G$ , where $d_{i j}$ denotes the distance between the vertices $v_{i}$ and $v_{j}$ . Suppose that $λ_{1} (D) \geq λ_{2} (D) \geq \dots \geq λ_{n} (D)$ are the distance spectrum of $G$ . The graph $G$ is said to be determined by its $D$ -spectrum if with respect to the distance matrix $D (G)$ , any graph having the same spectrum as $G$ is isomorphic to $G$ . We give the distance characteristic polynomial of some graphs with small diameter, and also prove that these graphs are determined...

Graphs with the Reduced Spectrum in the Unit Interval

Aleksandar Torgašev (1984)

Publications de l'Institut Mathématique

Green functions on self-similar graphs and bounds for the spectrum of the laplacian

Bernhard Krön (2002)

Annales de l’institut Fourier

Combining the study of the simple random walk on graphs, generating functions (especially Green functions), complex dynamics and general complex analysis we introduce a new method for spectral analysis on self-similar graphs.First, for a rather general, axiomatically defined class of self-similar graphs a graph theoretic analogue to the Banach fixed point theorem is proved. The subsequent results hold for a subclass consisting of “symmetrically” self-similar graphs which however is still more general then...

Gromov hyperbolic cubic graphs

Domingo Pestana, José Rodríguez, José Sigarreta, María Villeta (2012)

Open Mathematics

If X is a geodesic metric space and x 1; x 2; x 3 ∈ X, a geodesic triangle T = {x 1; x 2; x 3} is the union of the three geodesics [x 1 x 2], [x 2 x 3] and [x 3 x 1] in X. The space X is δ-hyperbolic (in the Gromov sense) if any side of T is contained in a δ-neighborhood of the union of the two other sides, for every geodesic triangle T in X. We denote by δ(X) the sharp hyperbolicity constant of X, i.e., δ(X) = inf {δ ≥ 0: X is δ-hyperbolic}. We obtain information about the hyperbolicity constant...

Group inverses of matrices with path graphs.

Catral, Minerva, Olesky, Dale D., van den Driessche, Pauline (2008)

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

Hadamard matrices and strongly regular graphs with the 3-e. c. adjacency property.

Bonato, Anthony, Holzmann, W.H., Kharaghani, Hadi (2001)

The Electronic Journal of Combinatorics [electronic only]

Hall exponents of Boolean matrices

Richard A. Brualdi, Bo Lian Liu (1990)

Czechoslovak Mathematical Journal

Horocyclic products of trees

Laurent Bartholdi, Markus Neuhauser, Wolfgang Woess (2008)

Journal of the European Mathematical Society

Let $T_{1}, \dots, T_{d}$ be homogeneous trees with degrees $q_{1} + 1, \dots, q_{d} + 1 \geq 3$ , respectively. For each tree, let $𝔥 : T_{j} \to ℤ$ be the Busemann function with respect to a fixed boundary point (end). Its level sets are the horocycles. The horocyclic product of $T_{1}, \dots, T_{d}$ is the graph $𝖣𝖫 (q_{1}, \dots, q_{d})$ consisting of all $d$ -tuples $x_{1} \dots x_{d} \in T_{1} \times \dots \times T_{d}$ with $𝔥 (x_{1}) + \dots + 𝔥 (x_{d}) = 0$ , equipped with a natural neighbourhood relation. In the present paper, we explore the geometric, algebraic, analytic and probabilistic properties of these graphs and their isometry groups. If $d = 2$ and $q_{1} = q_{2} = q$ then we obtain a Cayley graph of the...

Currently displaying 161 – 180 of 540

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Displaying 161 – 180 of 540

Graphs determined by their (signless) Laplacian spectra.

Graphs of diameter 2 with cyclic defect

Graphs whose energy does not exceed 3

Graphs whose minimal rank is two.

Graphs whose minimal rank is two: the finite fields case.

Graphs with given degree sequence and maximal spectral radius.

Graphs with least eigenvalue -2 attaining a convex quadratic upper bound for the stability number

Graphs with Least Eigenvalue at Least -sqrt(3)

Graphs with small diameter determined by their $D$ -spectra

Graphs with the Reduced Spectrum in the Unit Interval

Green functions on self-similar graphs and bounds for the spectrum of the laplacian

Gromov hyperbolic cubic graphs

Group inverses of matrices with path graphs.

Hadamard matrices and strongly regular graphs with the 3-e. c. adjacency property.

Hall exponents of Boolean matrices

Horocyclic products of trees

Hyperenergetic and Hypoenergetic Graphs

Hyperenergetic graphs and cyclomatic number

Improved bounds for the number of forests and acyclic orientations in the square lattice.

Improved upper bounds for the Laplacian spectral radius of a graph.

Currently displaying 161 – 180 of 540