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Crossing numbers of Sierpiński‐like graphs
Author(s) -
Klavžar Sandi,
Mohar Bojan
Publication year - 2005
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.20107
Subject(s) - combinatorics , mathematics , crossing number (knot theory) , sierpinski triangle , indifference graph , discrete mathematics , 1 planar graph , graph , chordal graph , fractal , mathematical analysis , intersection (aeronautics) , engineering , aerospace engineering
Crossing numbers of Sierpiński graphs S ( n , k ) and their regularizations S + ( n , k ) and S ++ ( n , k ) are studied. Drawings of these graphs are presented and proved to be optimal for S + ( n , k ) and S ++ ( n , k ) for every n ≥ 1 and k ≥ 1. The crossing numbers of these graphs are expressed in terms of the crossing number of K k +1 . These are the first nontrivial families of graphs of “fractal” type whose crossing number is known. © 2005 Wiley Periodicals, Inc. J Graph Theory