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Graphs and Combinatorics

, Volume 26, Issue 5, pp 629–646 | Cite as

Intriguing Sets of Vertices of Regular Graphs

  • Bart De Bruyn
  • Hiroshi Suzuki
Original Paper

Abstract

Intriguing and tight sets of vertices of point-line geometries have recently been studied in the literature. In this paper, we indicate a more general framework for dealing with these notions. Indeed, we show that some of the results obtained earlier can be generalized to larger classes of graphs. We also give some connections and relations with other notions and results from algebraic graph theory. One of the main tools in our study will be the Bose–Mesner algebra associated with the graph.

Keywords

Regular graph Tight set Intriguing set Completely regular code T-Design 

Mathematics Subject Classification (2000)

05E30 15A42 

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Copyright information

© Springer 2010

Authors and Affiliations

  1. 1.Department of Pure Mathematics and Computer AlgebraGhent UniversityGhentBelgium
  2. 2.Department of Mathematics and Computer ScienceInternational Christian UniversityTokyoJapan

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