Quotient-polynomial graphs

As a generalization of orbit-polynomial and distance-regular graphs, we introduce the concept of a quotient-polynomial graph. In these graphs every vertex u induces the same regular partition around u, where all vertices of each cell are equidistant from u. Some properties and characterizations of s...

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Vydané v:	Linear algebra and its applications Ročník 488; s. 363 - 376
Hlavný autor:	Fiol, M.A.
Médium:	Journal Article Publikácia
Jazyk:	English
Vydavateľské údaje:	Elsevier Inc 01.01.2016 Elsevier
Predmet:	05 Combinatorics 05C Graph theory 05E Algebraic combinatorics Classificació AMS Combinatorial analysis Combinatòria Distance-faithful partition Distance-regular graph Eigenvalues Grafs, Teoria de Graph quotient Graph theory Intersection numbers Matemàtica discreta Matemàtiques i estadística Orthogonal polynomials Quotient-polynomial graph Teoria de grafs Walk-regular partition Àrees temàtiques de la UPC 05E30 Intersection numbers 05C50 Graph quotient Quotient-polynomial graph Walk-regular partition Orthogonal polynomials Distance-regular graph Eigenvalues Distance-faithful partition
ISSN:	0024-3795, 1873-1856
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Popis
Shrnutí:	As a generalization of orbit-polynomial and distance-regular graphs, we introduce the concept of a quotient-polynomial graph. In these graphs every vertex u induces the same regular partition around u, where all vertices of each cell are equidistant from u. Some properties and characterizations of such graphs are studied. For instance, all quotient-polynomial graphs are walk-regular and distance-polynomial. Also, we show that every quotient-polynomial graph generates a (symmetric) association scheme.
ISSN:	0024-3795 1873-1856
DOI:	10.1016/j.laa.2015.09.053