Characterizing (l,m)-walk-regularity
A graph $\G$ with diameter $D$ and $d+1$ distinct eigenvalues is said to be {\it $(\ell,m)$-walk-regular}, for some integers $\ell\in[0,d]$ and $m\in[0,D]$, $\ell\ge m$, if the number of walks of length $i\in [0,\ell]$ between any pair of vertices at distance $j\in [0,m]$ depends only on the values...
| Autores: | , , |
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| Formato: | artículo |
| Fecha de publicación: | 2009 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/3007 |
| Acesso em linha: | https://hdl.handle.net/2117/3007 |
| Access Level: | acceso abierto |
| Palavra-chave: | Graph theory Combinatorics Distance-regular graph Walk-regular graph Adjacency matrix Spectrum Predistance polynomial Preintersection number Grafs, Teoria de Combinacions (Matemàtica) Classificació AMS::05 Combinatorics::05C Graph theory Classificació AMS::05 Combinatorics::05E Algebraic combinatorics Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs |
| Resumo: | A graph $\G$ with diameter $D$ and $d+1$ distinct eigenvalues is said to be {\it $(\ell,m)$-walk-regular}, for some integers $\ell\in[0,d]$ and $m\in[0,D]$, $\ell\ge m$, if the number of walks of length $i\in [0,\ell]$ between any pair of vertices at distance $j\in [0,m]$ depends only on the values of $i$ and $j$. In this paper we study some algebraic and combinatorial characterizations of $(\ell,m)$-walk-regularity based on the so-called predistance polynomials and the preintersection numbers. |
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