A graph G is said to be a simple cycle-distributed graph if G is a simple graph in which no two cycles have the same length. A graph G is said to be a simple maximum cycle-distributed graph (simple MCD-graph) if G is a simple cycle-distributed graph on n vertices which has the maximum possible number of edges. In this paper, we prove that ( 1 ) None of 2-connected non-planar graphs is a simple MCD-graph; ( 2) For each positive integer n(?){10, 11, 14, 15, 16, 21, 22}, there does not exist a simple MCD-graph on n verticas such that it is a 2-connected graph containing a subgraph homeomorphic to K_{4}. |