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Graphs with constant μ and μ

✍ Scribed by Edwin R. van Dam; Willem H. Haemers

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
803 KB
Volume
182
Category
Article
ISSN
0012-365X

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✦ Synopsis

A graph G has constant # = #(G) if any two vertices that are not adjacent have # common neighbours. G has constant/~ and fi if G has constant ~ = #(G), and its complement G has constant fi = #(G). If such a graph is regular, then it is strongly regular, otherwise precisely two vertex degrees occur. We shall prove that a connected graph has constant # and fi if and only if it has two distinct nonzero Laplace eigenvalues. This leads to strong conditions for existence. Several constructions are given and characterized. A list of feasible parameter sets for graphs with at most 40 vertices is generated.

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