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I‐graphs and the corresponding configurations
Author(s) -
Boben Marko,
Pisanski Tomaž,
Žitnik Arjana
Publication year - 2005
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.20054
Subject(s) - mathematics , combinatorics , bipartite graph , chordal graph , odd graph , indifference graph , pathwidth , cograph , discrete mathematics , maximal independent set , isomorphism (crystallography) , 1 planar graph , graph , line graph , chemistry , crystal structure , crystallography
We consider the class of I‐graphs I ( n,j,k ), which is a generalization over the class of the generalized Petersen graphs. We study different properties of I‐graphs, such as connectedness, girth, and whether they are bipartite or vertex‐transitive. We give an efficient test for isomorphism of I‐graphs and characterize the automorphism groups of I‐graphs. Regular bipartite graphs with girth at least 6 can be considered as Levi graphs of some symmetric combinatorial configurations. We consider configurations that arise from bipartite I‐graphs. Some of them can be realized in the plane as cyclic astral configurations, i.e., as geometric configurations with maximal isometric symmetry. © 2005 Wiley Periodicals, Inc.