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On the eigenvalues of Jordan products

Martins, E.A.; Silva, F.C.
Fonte: Elsevier Publicador: Elsevier
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
36.49%
This paper studies the possible eigenvalues of the Jordan product XA+AX, when A is fixed and X varies. © 2002 Elsevier Science Inc. All rights reserved.; Centro de Estruturas Lineares e Combinatórias; FCT

Main eigenvalues and (κ, τ)-regular sets

Cardoso, D.M.; Sciriha, I.; Zerafa, C.
Fonte: Elsevier Publicador: Elsevier
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
36.6%
A (κ, τ)-regular set is a subset of the vertices of a graph G, inducing a κ-regular subgraph such that every vertex not in the subset has τ neighbors in it. A main eigenvalue of the adjacency matrix A of a graph G has an eigenvector not orthogonal to the all-one vector j. For graphs with a (κ, τ)-regular set a necessary and sufficient condition for an eigenvalue be non-main is deduced and the main eigenvalues are characterized. These results are applied to the construction of infinite families of bidegreed graphs with two main eigenvalues and the same spectral radius (index) and some relations with strongly regular graphs are obtained. Finally, the determination of (κ, τ)-regular sets is analyzed. © 2009 Elsevier Inc. All rights reserved.; CEOC; FCT; FEDER/POCI 2010; University of Malta

Eigenvalues of a H-generalized join graph operation constrained by vertex subsets

Cardoso, Domingos M.; Martins, Enide A.; Robbiano, Maria; Rojo, Oscar
Fonte: Elsevier Publicador: Elsevier
Tipo: Artigo de Revista Científica
ENG
Relevância na Pesquisa
36.6%
A generalized H-join operation of a family of graphs G1, . . . , Gp, where H has order p, constrained by a family of vertex subsets Si ⊆V(Gi), i = 1, . . . , p, is introduced. When each vertex subset Si is (ki, τi)-regular, it is deduced that all non-main adjacency eigenvalues of Gi , different from ki−τi , remain as eigenvalues of the graph G obtained by this operation. If each Gi is ki-regular and all the vertex subsets are such that Si = V(Gi), the H-generalized join constrained by these vertex subsets coincides with the H-join operation. Furthermore, some applications on the spread of graphs are presented.