摘要
设ｒ是不小于４的偶数，一个阶为ｖ（ｖ为偶数）的偶图Ｇ称为唯一ｒ－偶泛圈图，如果对每一偶数ｔ（ｒ≤ｔ≤ｖ），Ｇ恰含一ｔ圈，而不含长小于ｒ的圈。若Ｇ是唯一ｒ－偶泛圈图，则称Ｇ为ｒ－ＵＢ图，设Ｇ是ｒ－ＵＢ图，Ｃ是Ｇ的Ｈａｍｉｌｔｏｎ圈，本文约定Ｇ中不在圈Ｃ上的边全画在Ｃ的内部，并称这些边为Ｇ的桥．如果Ｇ的一条桥的两个端点在圈Ｃ上分离另一条桥的两个端点，则称这两条桥是交叉的．有ｎ对交叉桥的ｒ－ＵＢ图称为ｒ－ＵＢ［ｎ］图．本文确定了所有ｒ－ＵＢ［１］图．
Let integer r≥4 be even. A bipartite graph G of even order v is said to be uniquely r-bipancyclic if G contains exactly one cycle of every even length t,r≤t≤v, and G contains no cycle of length less than r. If G is a uniquely r-bipancyclic graph, then G is called an r-UB-graph.Let G be an r-UB-graph and C the Hamiton cycle of G. We assume that the edges of G other than those edges of C are drawn in the interior of C, and we call these edges the bridges of G. Two bridges B and B' are said to be cross if the end venices of one bridge separate the end venices of the other. If the total number of distinct pairs of cross bridges of G is n, then we call G an r-UB[n]-graph. In this paper, the class of r-UB[1]-graphs is completely determined.
出处
《上海师范大学学报（自然科学版）》
1996年第2期19-27,共9页
Journal of Shanghai Normal University(Natural Sciences)
关键词
圈
偶图
r-UB图
图
cycle
bipartite graph
r-UB graph
r-UB[1]-graph
