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Indexed by:期刊论文

Date of Publication:2008-01-01

Journal:ARS COMBINATORIA

Included Journals:SCIE

Volume:86

Page Number:57-64

ISSN No.:0381-7032

Key Words:crossing number; cubic graph; flower snark

Abstract:For odd n >= 5, the Flower Snark F-n = (V, E) is a simple undirected cubic graph with 4n vertices, where V = {a(i) : 0 <= i <= n - 1} U {b(i) : 0 <= i <= n - 1} boolean OR {c(i) : 0 <= i <= 2n - 1} and E={b(i)b((i+i)) (mod n) : 0 <= i <= n-1}boolean OR{c(i)c((i+1) mod 2n) : 0 <= i <= 2n - 1} boolean OR {a(i)b(i), a(i)c(i), a(i)c(n+i) : 0 <= i <= n - 1}. For n = 3 or even n >= 4, F-n is called the related graph of Flower Snark. We show that the crossing number of F-n equals n - 2 if 3 <= n <= 5, and n if n >= 6.