کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4649696 1342464 2008 20 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Further results on the enumeration of hamilton paths in Cayley digraphs on semidirect products of cyclic groups
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات گسسته و ترکیبات
پیش نمایش صفحه اول مقاله
Further results on the enumeration of hamilton paths in Cayley digraphs on semidirect products of cyclic groups
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Mathematics - Volume 308, Issue 10, 28 May 2008, Pages 1889–1908
نویسندگان
,