Distance-regular graphs with a 1 or c 2 at least half the valency

Jack H. Koolen; Jongyook Park

doi:10.1016/j.jcta.2011.11.001

Distance-regular graphs with a ₁ or c ₂ at least half the valency

Jack H. Koolen
, Jongyook Park

Pohang University of Science and Technology

Research output: Contribution to journal › Article › peer-review

25 Scopus citations

Abstract

In this paper, we study the distance-regular graphs Γ that have a pair of distinct vertices, say x and y, such that the number of common neighbors of x and y is about half the valency of Γ. We show that if the diameter is at least three, then such a graph, besides a finite number of exceptions, is a Taylor graph, bipartite with diameter three or a line graph.

Original language	English
Pages (from-to)	546-555
Number of pages	10
Journal	Journal of Combinatorial Theory. Series A
Volume	119
Issue number	3
DOIs	https://doi.org/10.1016/j.jcta.2011.11.001
State	Published - Apr 2012

Keywords

Distance-regular graphs
Line graphs
Taylor graphs

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10.1016/j.jcta.2011.11.001

Cite this

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title = "Distance-regular graphs with a 1 or c 2 at least half the valency",

abstract = "In this paper, we study the distance-regular graphs Γ that have a pair of distinct vertices, say x and y, such that the number of common neighbors of x and y is about half the valency of Γ. We show that if the diameter is at least three, then such a graph, besides a finite number of exceptions, is a Taylor graph, bipartite with diameter three or a line graph.",

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AB - In this paper, we study the distance-regular graphs Γ that have a pair of distinct vertices, say x and y, such that the number of common neighbors of x and y is about half the valency of Γ. We show that if the diameter is at least three, then such a graph, besides a finite number of exceptions, is a Taylor graph, bipartite with diameter three or a line graph.

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KW - Line graphs

KW - Taylor graphs

UR - https://www.scopus.com/pages/publications/81255164786

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DO - 10.1016/j.jcta.2011.11.001

M3 - Article

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IS - 3

ER -

Distance-regular graphs with a ₁ or c ₂ at least half the valency

Abstract

Keywords

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