30 documents found, page 1 of 3
On spectral invariants of the α-mixed adjacency matrix
Andrade, Enide; Lenes, Eber; Pizarro Pamela; Robbiano, María; Rodríguez, JonnathanLet Gˆ be a mixed graph and α∈[0,1]. Let Dˆ(Gˆ) and Aˆ(Gˆ) be the diagonal matrix of vertex degrees and the mixed adjacency matrix of Gˆ, respectively. The α-mixed adjacency matrix of Gˆ is the matrix Aˆα(Gˆ)=αDˆ(Gˆ)+(1−α)Aˆ(Gˆ).We study some properties of Aˆα(Gˆ) associated with some type of mixed graphs, namely quasi-bipartite and pre-bipartite mixed graphs. A spectral characterization for pre-bipartite and s...
On the Eigenvectors of Generalized Circulant Matrices
Andrade, Enide; Carrasco-Olivera, Dante; Manzaneda, CristinaIn \cite{Mourad}, Kaddoura and Mourad, in order to widen the scope of the class of circulant matrices, (see \cite{Davis}), constructed circulant-like matrices that were called generalized weighted circulant matrices. These matrices form a class of matrices generated by generalized permutation matrices corresponding to a subgroup of some permutation group. The characteristic polynomials, eigenvalues and eigenvec...
Perron values and classes of trees
Andrade, Enide; Ciardo, Lorenzo; Dahl, GeirThe bottleneck matrix $M$ of a rooted tree $T$ is a combinatorial object encoding the spatial distribution of the vertices with respect to the root. The spectral radius of $M$, known as the Perron value of the rooted tree, is closely related to the theory of the algebraic connectivity. In this paper, we investigate the Perron values of various classes of rooted trees by making use of combinatorial and linear-al...
Some families of integral mixed graphs
Andrade, Enide; Bonifácio, Andréa Soares; Robbiano, María; Rodríguez, Jonnathan; Tapia, KatherineA mixed graph $\hat{G}$ is a graph where two vertices can be connected by an edge or by an arc (directed edge). The adjacency matrix , $\hat{A}(\hat{G})$, of a mixed graph has rows and columns indexed by the set of vertices of $\hat{G}$, being its $\{u,v\}$-entry equal to $1$ (respectively, $-1$) if the vertex $u$ is connected by an edge (respectively, an arc) to the vertex $v,$ and $0$ otherwise. These graphs ...
On the spectral radius of the generalized adjacency matrix of a digraph
Baghipur, Maryam; Ganie, Hilal A.; Ghorbani, Modjtaba; Andrade, EnideLet $ D$ be a strongly connected digraph and $\alpha\in [0,1].$ In [J. P. Liu, X. Z. Wu, J. S. Chen and B. L. Liu, The $ A_{\alpha} $ spectral radius characterization of some digraphs, Linear Algebra Appl. 563 (2019) 63--74] the matrix $ A_{\alpha}(D)=\alpha Deg(D)+(1-\alpha)A(D),$ where $ A(D)$ and $Deg(D)$ are the adjacency matrix and the diagonal matrix of the out-degrees of $D,$ respectively, was defined. I...
The 9th International Conference on Matrix Analysis and Applications (ICMAA) Av...
Andrade, Enide; Lemos, RuteThe 9th International Conference on Matrix Analysis and Applications (ICMAA 2022) was held at the Department of Mathematics of the University of Aveiro in Aveiro, Portugal, June 15–17, 2022. The purpose of this meeting was to stimulate research and interaction among mathematicians working in all aspects of linear and multilinear algebra, matrix analysis, graph theory, and related applications, providing an oppo...
On circulant like matrices properties involving Horadam, Fibonacci, Jacobsthal ...
Andrade, Enide; Carrasco-Olivera, Dante; Manzaneda, CristinaIn this work a new type of matrix called circulant-like matrix is introduced. This type of matrix includes the classical k-circulant matrix, introduced in [4], in a natural sense. Its eigenvalues and its inverse and some other properties are studied, namely, it is shown that the inverse of a matrix of this type is also a matrix of this type and that its first row is the unique solution of a certain system of li...
Extremal graphs for Estrada indices
Andrade, Enide; Lenes, Eber; Mallea-Zepeda, Exequiel; Robbiano, María; Rodríguez Z., JonnathanLet $\mathcal{G}$ be a simple undirected connected graph. The signless Laplacian Estrada, Laplacian Estrada and Estrada indices of a graph $\mathcal{G}$ is the sum of the exponentials of the signless Laplacian eigenvalues, Laplacian eigenvalues and eigenvalues of $\mathcal{G}$, respectively. The present work derives an upper bound for the Estrada index of a graph as a function of its chromatic number, in the fa...
On the energy of singular and non singular graphs
Andrade, Enide; Carmona, Juan R.; Poveda, Alex; Robbiano, MaríaLet $G$ be a simple undirected graph with $n$ vertices, $m$ edges, adjacency matrix $A$, largest eigenvalue $\rho$ and nullity $\kappa$. The energy of $G,$ $\mathcal{E}(G)$ is the sum of its singular values. In this work lower bounds for $\mathcal{E}(G)$ in terms of the coefficient of $\mu^{\kappa}$ in the expansion of characteristic polynomial, $p(\mu)=\det{(\mu I-A)}$ are obtained. In particular one of the bo...
A lower bound for the energy of hypoenergetic and non hypoenergetic graphs
Andrade, Enide; R. Carmona, Juan; Infante, Geraldine; Robbiano, MaríaLet $G$ be a simple undirected graph with $n$ vertices and $m$ edges. The energy of $G,$ $\mathcal{E}(G)$ corresponds to the sum of its singular values. This work obtains lower bounds for $\mathcal{E}(G)$ where one of them generalizes a lower bound obtained by Mc Clelland in $1971$ to the case of graphs with given nullity. An extension to the bipartite case is given and, in this case, it is shown that the lower...