关于简单MCD图

设G是阶为n的简单图，若G中没有两个等长圈且具有最大可能的边数，则称G为简单MCD图。本文通过引进路分解概念给出了两个关于图中圈数的结果并应用它们证明了下述定理：若G是简单MCD图，则G不是2连通可平面图且对所有整数n，除七个例外，G不是阶为n的含有同胚于K4的2连通图。

On Simple MCD-Graphs

A simple graph G on n vettices is said to be a simple MCD-graph if G has no two cyties having the same length and has the maximum possible number of edges.Two results of the number of cy cles in G are given by introdueing the Concept of a path decomposition and by them,the following theorem is proved:If G is a simple MCD-graph,then G is not a 2-connected planar graph and for all n except seven integer,G is not a 2-connected graph on n vertices containing a subgraph homeomor phic to K_4.