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Graph operations and Laplacian eigenpolytopes
Padrol Sureda, Arnau; Pfeifle, Julián
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada II; Universitat Politècnica de Catalunya. MD - Matemàtica Discreta
We introduce the Laplacian eigenpolytopes ("L-polytopes") associated to a simple undirected graph G, investigate how they change under basic operations such as taking the union, join, complement, line graph and cartesian product of graphs, and show how several "famous" polytopes arise as L-polytopes of "famous" graphs. Eigenpolytopes have been previously introduced by Godsil, who studied them in detail in the context of distance-regular graphs. Our focus on the Laplacian matrix, as opposed to the adjacency matrix of G, permits simpler proofs and descriptions of the result of operations on not necessarily distance-regular graphs. Additionally, it motivates the study of new operations on polytopes, such as the Kronecker product. Thus, we open the door to a detailed study of how combinatorial properties of G are reflected in its L-polytopes. Subsequent papers will use these tools to construct interesting polytopes from interesting graphs, and vice versa.
Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
Spectrum analysis
Laplacian operator
Polytopes
Eigenvalues
Algebras, Linear
Anàlisi espectral
Politops
Àlgebra lineal
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
info:eu-repo/semantics/publishedVersion
info:eu-repo/semantics/conferenceObject
         

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