The Structure Of A Kind Of Maximal Critically H_Connected Graphs

A h_connected G is a critical if G- v is not h_connected for every A critical h-connected G is maximal if the addition of any new edge results in a graph which is not critical connected .The new structure of all maximal critical h_connected graphs with minimum degree and a procedure for constructing every h_connected graph are determined.In this paper we prove the following main theorem:Theorem 4 Let h be an even.Then G is a maximal critical h_connected graph with minimum degree if and only if or G can be constructed by a sequence of pasting according to the following conditions:first H is obtained by asequence of pasting along cliques of elements then paste H onto t_copies of where is a set of some complete graphs with order greater h:(a) Every vertex of complete graphs belongs to either a h_Cliqe of the elements of or a h_Cliqe of .(b) If a h_clique is used to paste two elements of then it is used only once.(c) If are distinct h_cliques, such that every is used either to paste elements of or to paste and if ,then T is not usded to paste the elements of (d) If and z belings to H_clique of elements of then...