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Spectral behavior of some graph and digraph compositions
dc.contributor.author | Boulet, Romain |
dc.date.accessioned | 2011-05-09T15:22:54Z |
dc.date.available | 2011-05-09T15:22:54Z |
dc.date.issued | 2011 |
dc.identifier.citation | Boulet, Romain. Spectral behavior of some graph and digraph compositions. A: International Workshop on Optimal Networks Topologies. "Proceedings of the 3rd International Workshop on Optimal Networks Topologies IWONT 2010". Barcelona: Iniciativa Digital Politècnica, 2011, p. 121-143. |
dc.identifier.isbn | 978-84-7653-565-3 |
dc.identifier.uri | http://hdl.handle.net/2099/10370 |
dc.description.abstract | Let G be a graph of order n the vertices of which are labeled from 1 to n and let $G_1$, · · · ,$G_n$ be n graphs. The graph composition G[$G_1$, · · · ,$G_n$] is the graph obtained by replacing the vertex i of G by the graph Gi and there is an edge between u ∈ $G_i$ and v ∈ $G_j$ if and only if there is an edge between i and j in G. We first consider graph composition G[$K_k$, · · · ,$K_k$] where G is regular and $K_k$ is a complete graph and we establish some links between the spectral characterisation of G and the spectral characterisation of G[$K_k$, · · · ,$K_k$]. We then prove that two non isomorphic graphs G[$G_1$, · · ·$G_n$] where $G_i$ are complete graphs and G is a strict threshold graph or a star are not Laplacian-cospectral, giving rise to a spectral characterization of these graphs. We also consider directed graphs, especially the vertex-critical tournaments without non-trivial acyclic interval which are tournaments of the shape t[$\overrightarrow{C}_{k_1}$, · · · ,$\overrightarrow{C}_{k_m}$], where t is a tournament and $\overrightarrow{C}_{k_i}$ is a circulant tournament. We give conditions to characterise these graphs by their spectrum. |
dc.format.extent | 23 p. |
dc.language.iso | eng |
dc.publisher | Iniciativa Digital Politècnica |
dc.relation.ispartof | International Workshop on Optimal Networks Topologies |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs |
dc.subject.lcsh | Directed graphs |
dc.subject.lcsh | Graph theory |
dc.title | Spectral behavior of some graph and digraph compositions |
dc.type | Conference report |
dc.subject.lemac | Grafs, Teoria de |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::05 Combinatorics::05C Graph theory |
dc.rights.access | Open Access |
local.citation.author | Boulet, Romain |
local.citation.contributor | International Workshop on Optimal Networks Topologies |
local.citation.pubplace | Barcelona |
local.citation.publicationName | Proceedings of the 3rd International Workshop on Optimal Networks Topologies IWONT 2010 |
local.citation.startingPage | 121 |
local.citation.endingPage | 143 |
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3er. 2010 [27]
Facultat de Matemàtiques i Estadística, Universitat Politècnica de Catalunya, Barcelona, 9-11 June 2010