Graphs with constant μ and μ

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Abstract

A graph G has constant u = u(G) if any two vertices that are not adjacent have u common neighbours. G has constant u and u if G has constant u = u(G), and its complement G has constant u = u(G). If such a graph is regular, then it is strongly regular, otherwise precisely two vertex degrees occur. We shall prove that a graph has constant u and u if and only if it has two distinct restricted Laplace eigenvalues. Bruck-Ryser type conditions are found. Several constructions are given and characterized. A list of feasible parameter sets for graphs with at most 40 vertices is generated.
Original languageEnglish
PublisherUnknown Publisher
Number of pages14
VolumeFEW 688
Publication statusPublished - 1995

Publication series

NameResearch memorandum / Tilburg University, Faculty of Economics and Business Administration
VolumeFEW 688

Keywords

  • Graphs
  • Eigenvalues
  • mathematics

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    van Dam, E. R., & Haemers, W. H. (1995). Graphs with constant μ and μ. (Research memorandum / Tilburg University, Faculty of Economics and Business Administration; Vol. FEW 688). Unknown Publisher.