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Crossing numbers of Sierpiński-like graphs

✍ Scribed by Sandi Klavžar; Bojan Mohar

Publisher
John Wiley and Sons
Year
2005
Tongue
English
Weight
161 KB
Volume
50
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

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

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