一类几乎唯一泛圈图

设G是阶为n的简单Hamilton图．若存在m(3(?)m

A Class of Almost Uniquely Pancyclic Graphs

Let $G$ be a simple Hamilton graph with $n$ vertices. If there exists $m(3\leq m<n)$ such that $G$ contains exactly one cycle of length $l$ for every $l\in \{3,4,\cdots,n\}-\{m\}$ and contains no cycle of length of $m$, then $G$ is called almost uniquely pancyclic graph. Let ${\it\Gamma}_k^0$ denote the set of simple Hamilton graphs with $n+k$ edges and $\frac{k^2+5k-2}{2}$ cycles. In this paper all almost uniquely pancyclic graphs in ${\it\Gamma}_k^0$ are determined and are proved to be simple MCD graphs.