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Citació: Dalfo, C. [et al.]. On almost distance-regular graphs. "Journal of combinatorial theory. Series A", 2010.
Títol: On almost distance-regular graphs
Autor: Dalfó Simó, Cristina Veure Producció científica UPC; Van Dam, Edwin; Fiol Mora, Miquel Àngel Veure Producció científica UPC; Garriga Valle, Ernest Veure Producció científica UPC; Gorissen, Bram
Data: 2010
Tipus de document: Article
Resum: Distance-regular graphs are a key concept in Algebraic Combinatorics and have given rise to several generalizations, such as association schemes. Motivated by spectral and other algebraic characterizations of distance-regular graphs, we study ‘almost distanceregular graphs’. We use this name informally for graphs that share some regularity properties that are related to distance in the graph. For example, a known characterization of a distance-regular graph is the invariance of the number of walks of given length between vertices at a given distance, while a graph is called walk-regular if the number of closed walks of given length rooted at any given vertex is a constant. One of the concepts studied here is a generalization of both distance-regularity and walk-regularity called m-walkregularity. Another studied concept is that of m-partial distanceregularity or, informally, distance-regularity up to distance m. Using eigenvalues of graphs and the predistance polynomials, we discuss and relate these and other concepts of almost distance-regularity, such as their common generalization of ( ,m)-walk-regularity. We introduce the concepts of punctual distance-regularity and punctual walk-regularity as a fundament upon which almost distanceregular graphs are built. We provide examples that are mostly taken from the Foster census, a collection of symmetric cubic graphs. Two problems are posed that are related to the question of when almost distance-regular becomes whole distance-regular. We also give several characterizations of punctually distance-regular graphs that are generalizations of the spectral excess theorem.
ISSN: 0097-3165
URI: http://hdl.handle.net/2117/11111
DOI: 10.1016/j.jcta.2010.10.005
Apareix a les col·leccions:COMBGRAF - Combinatòria, Teoria de Grafs i Aplicacions. Articles de revista
Departaments de Matemàtica Aplicada. Articles de revista
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