摘要
The bounds are obtained for the average crosscap number. Let G be a graph which is not a tree. It is shown that the average crosscap number of G is not less thanβ(G)-1/2β(G)-1β(G) and not larger thanβ(G). Furthermore, we also describe the structure of the graphs which attain the bounds of the average crosscap number.
The bounds are obtained for the average crosscap number. Let G be a graph which is not a tree. It is shown that the average crosscap number of G is not less than 2 β(G?1/2 β(G?1 β(G) and not larger than β(G). Furthermore, we also describe the structure of the graphs which attain the bounds of the average crosscap number.
基金
This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 60373030,10751013)
