一类几乎唯一泛圈图  

A CLASS OF ALMOST UNIQUELY PANCYCLIC GRAPHS

作　　者：施永兵[1] 

机构地区：[1]上海师范大学数理信息学院,上海200234

出　　处：《系统科学与数学》2006年第4期433-439,共7页Journal of Systems Science and Mathematical Sciences

基　　金：上海市教委科技发展基金(04DB25)资助课题

摘　　要：设G是阶为n的简单Hamilton图．若存在m(3(?)m<n)使对每个l∈{3,4,…,n}-{m},G恰有一个长为l的圈且不含长为m的圈,则称G是几乎唯一泛圈图．用Г0k表示具有n+k条边和恰有(k2+5k-2)/2个圈的简单H图的集合．作者确定了Г0k中所有几乎唯一泛圈图,并证明这些图都是简单MCD图．Let G be a simple Hamilton graph with n vertices. If there exists m（3 ≤ m 〈 n） such that G contains exactly one cycle of length l for every lε {3, 4,……, n} - {m} and contains no cycle of length of m, then G is called almost uniquely pancyclic graph. Let Г^ok denote the set of simple Hamilton graphs with n ＋ k edges and k^2＋5k-2/2 cycles. In this paper all almost uniquely pancyclic graphs in Г^ok are determined and are proved to be simple MCD graphs.

关 键 词：圈 几乎唯一泛圈图 简单MCD图 

分 类 号：O157.5[理学—数学]