کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4649696 | 1342464 | 2008 | 20 صفحه PDF | دانلود رایگان |

First, let m and n be positive integers such that n is odd and gcd(m,n)=1gcd(m,n)=1. Let G be the semidirect product of cyclic groups given by G=Z8m⋊Z2n=〈x,y:x8m=1,y2n=1,andyxy-1=x4m+1〉. Then the number of hamilton paths in Cay(G:x,y)Cay(G:x,y) (with initial vertex 1) is one fewer than the number of visible lattice points that lie on the closed quadrilateral whose vertices in consecutive order are (0,0)(0,0), (4mn2+2n,16m2n)(4mn2+2n,16m2n), (n,4m)(n,4m), and (0,8m)(0,8m). Second, let m and n be positive integers such that n is odd. Let G be the semidirect product of cyclic groups given by G=Z4m⋊Z2n=〈x,y:x4m=1,y2n=1,andyxy-1=x2m-1〉. Then the number of hamilton paths in Cay(G:x,y)Cay(G:x,y) (with initial vertex 1) is (3m-1)n+m⌊(n+1)/3⌋+1(3m-1)n+m⌊(n+1)/3⌋+1.
Journal: Discrete Mathematics - Volume 308, Issue 10, 28 May 2008, Pages 1889–1908