The energy of signed graph is the sum of the absolute values of the eigenvalues of its adjacency matrix. Two signed graphs are said to be equienergetic if they have same energy. In the literature the construction of equienergetic signed graphs are reported. In this paper we obtain the characteristic polynomial and energy of the join of two signed graphs and thereby we give another construction ...

Altan derivatives of polycyclic conjugated hydrocarbons were recently introduced and studied in theoretical organic chemistry. We now provide a generalization of the altan concept, applicable to any graph. Several earlier noticed topological properties of altan derivatives of polycyclic conjugated hydrocarbons are shown to be the properties of all altan derivatives of all graphs. Among these ar...

In this work we continue the investigation of different approaches to conception and modeling of composite materials. The global method we focus on, is called ’stochastic homogenization’. In this approach, the classical deterministic homogenization techniques and procedures are used to compute the macroscopic parameters of a composite starting from its microscopic properties. The stochastic par...

Some combinatorial and spectral properties of König-Egerváry (K-E) graphs are presented. In particular, some new combinatorial characterizations of K-E graphs are introduced, the Laplacian spectrum of particular families of K-E graphs is deduced, and a lower and upper bound on the largest and smallest adjacency eigenvalue, respectively, of a K-E graph are determined.

We prove lower bounds on the largest and second largest eigenvalue of the adjacency matrix of connected bipartite graphs and give necessary and sufficient conditions for equality. We give several examples of classes of graphs that are optimal with respect to the bounds. We prove that BIBD-graphs are characterized by their eigenvalues. Finally we present a new bound on the expansion coefficient ...

Many combinatorial configurations (for example, perfect codes, latin squares and hypercubes, combinatorial designs and their q-ary generalizations — subspace designs) can be defined as an eigenfunction on a graph with some discrete restrictions. The study of these configurations often leads to the question about the minimum possible difference between two configurations from the same class (it ...

We consider the following problem: When do alternate eigenvalues taken from a matrix ensemble themselves form a matrix ensemble? More precisely, we classify all weight functions for which alternate eigenvalues from the corresponding orthogonal ensemble form a symplectic ensemble, and similarly classify those weights for which alternate eigenvalues from a union of two orthogonal ensembles forms ...

Let (X,S) be an association scheme where X is a finite set and S is a partition of X × X. We say that (X,S) is symmetric if σs is symmetric for each s ∈ S where σs is the adjacency matrix of s, and integral if ⋃ s∈S ev(σs) ⊆ Z where ev(σs) is the set of all eigenvalues of σs. For an association scheme (X,T ) we say that (X,T ) is a fusion of (X,S) if each element of T is a union of elements of ...

We present the first results for recovering word-word dependencies from a probabilistic parser for Portuguese trained on and evaluated against human annotated syntactic analyses. We use the Floresta Sintá(c)tica with the Bikel multi-lingual parsing engine and evaluate performance on both PARSEVAL and unlabeled dependencies. We explore several configurations, both in terms of parameterizing the ...

A regular network is a network with one kind of node and one kind of coupling. We show that a codimension one bifurcation from a synchronous equilibrium in a regular network is at linear level isomorphic to a generalized eigenspace of the adjacency matrix of the network, at least when the dimension of the internal dynamics of each node is greater than 1. We also introduce the notion of a produc...