1999/07/08 by Dmitry Jakobson, Jakobson, Dmitry, Igor Rivin +1 · 6 citations
Mathematics · Physics and Astronomy · #05C35 #05C85 #49K35 #90C35 #Combinatorics (math.CO) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Rings and Algebras (math.RA) #Spectral Theory (math.SP) #math-ph #math.CO #math.MP #math.RA #math.SP #msc:05C35 #msc:05C85 #msc:49K35 #msc:90C35
paper · pdf · doi:10.48550/arxiv.math/9907050
June 1998 Preprint
arxiv created 1999/07/08 · arxiv updated 2009/11/30
In this paper we are concerned with various graph invariants (girth, diameter, expansion constants, eigenvalues of the Laplacian, tree number) and their analogs for weighted graphs -- weighing the graph changes a combinatorial problem to one in analysis. We study both weighted and unweighted graphs which are extremal for these invariants. In the unweighted case we concentrate on finding extrema among all (usually) regular graphs with the same number of vertices; we also study the relationships between such graphs.