Release Time:2019-03-10  Hits:

Indexed by: Journal Article

Date of Publication: 2008-01-01

Journal: ARS COMBINATORIA

Included Journals: SCIE

Volume: 86

Page Number: 57-64

ISSN: 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.