Please use this identifier to cite or link to this item
http://hdl.handle.net/10773/4309

title:  Spectral results on graphs with regularity constraints 
authors:  Cardoso, D.M. Rama, P. 
keywords:  Equitable partitions Graph spectra Graph theory Strongly regular graphs Constrained optimization Eigenvalues and eigenfunctions Matrix algebra 
issue date:  2007 
publisher:  Elsevier 
abstract:  Graphs with (k, τ)regular sets and equitable partitions are examples of graphs with regularity constraints. A (k, τ)regular set of a graph G is a subset of vertices S ⊆ V(G) inducing a kregular subgraph and such that each vertex not in S has τ neighbors in S. The existence of such structures in a graph provides some information about the eigenvalues and eigenvectors of its adjacency matrix. For example, if a graph G has a (k1, τ1)regular set S1 and a (k2, τ2)regular set S2 such that k1  τ1 = k2  τ2 = λ, then λ is an eigenvalue of G with a certain eigenvector. Additionally, considering primitive strongly regular graphs, a necessary and sufficient condition for a particular subset of vertices to be (k, τ)regular is introduced. Another example comes from the existence of an equitable partition in a graph. If a graph G, has an equitable partition π then its line graph, L(G), also has an equitable partition, over(π, ̄), induced by π, and the adjacency matrix of the quotient graph L (G) / over(π, ̄) is obtained from the adjacency matrix of G/π. © 2006 Elsevier Inc. All rights reserved. 
URI:  http://hdl.handle.net/10773/4309 
ISSN:  00243795 
publisher version/DOI:  http://www.sciencedirect.com/science/article/pii/S0024379506004526 
source:  Linear Algebra and Its Applications 
appears in collections  MAT  Artigos

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.
