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Some new large (Δ, 3)‐graphs
Author(s) -
Gómez J.
Publication year - 2009
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/net.20254
Subject(s) - degree (music) , combinatorics , computer science , indifference graph , pathwidth , metric dimension , table (database) , trapezoid graph , mathematics , chordal graph , discrete mathematics , 1 planar graph , graph , line graph , data mining , physics , acoustics
We study the problem of finding large graphs with given degree Δ and diameter D = 3; that is, the construction of graphs with number of vertices as large as possible for a given degree Δ and diameter D = 3. There are two general methods to obtain large graphs: computer search and analytic methods. In this article, new ideas are proposed for analytic methods which allow us to improve the values for the entries (12,3), (13,3), and (14,3) in the table of the largest known (Δ, D )‐graphs. © 2008 Wiley Periodicals, Inc. NETWORKS, 2009