On The Length Of Longest Cycles And Co-diameter Of K-Connected Graphs

This thesis consists of three parts, The first part, is a comprehensive introduction to the background of the research and the results on the longest cycles and co-diameter of k-connected graphs we presented in the thesis. The second part and the third part, are on the low bounds of circumferences and co-diameters of k-connected graphs, respectively.Define a(G):=α,k(G):=k,n:=▕V(G)▕. In 1972, Chvatal and Erdos [15]proved two well-known theorems:ifα≤k, then G is hamiltonian; ifα