An eigenvalue characterization of antipodal distance-regular graphs

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Title:	An eigenvalue characterization of antipodal distance-regular graphs
Author:	Fiol Mora, Miquel Àngel
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV; Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions
Abstract:	Let $\Gamma$ be a regular (connected) graph with $n$ vertices and $d+1$ distinct eigenvalues. As a main result, it is shown that $\Gamma$ is an $r$-antipodal distance-regular graph if and only if the distance graph $\Gamma_d$ is constituted by disjoint coies of the complete graph $K_r$, with $r$ satisfying an expression in terms of $n$ and the distinct eigenvalues.
Abstract:	Peer Reviewed
Subject(s):	-Graph theory -Combinatorics -Antipodal distance-regular graph -Eigenvalues -Alternating polynomials -Grafs, Teoria de -Combinacions (Matemàtica) -Classificació AMS::05 Combinatorics::05C Graph theory -Classificació AMS::05 Combinatorics::05E Algebraic combinatorics
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Document type:	Article
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