A t-container Ct(u,v)is a set of t internally disjoint paths between two distinct vertices u and v in a graph G,i.e.,Ct(u,v)={P1,P2,…,Pt}.Moreover,if V(P1)U V(P2)U …U V(Pt)=V(G)then Ct(u,v)is called a spanning t-container,denoted by Csct(u,v).The length of Csct(u,v)={P1,P2,…,Pt} is l(Csct(u,v))=max{l(Pi)|1 ≤ i ≤ t}.A graph G is spanning t-connected if there exists a spanning t-container between any two distinct vertices u and v in G.Assume that u and v are two distinct vertices in a spanning t-connected graph G.Let Dsct(u,v)be the collection of all Csct(u,v)'s.Define the spanning t-wide distance between u and v in G,dsct(u,v)=min{l(Csct(u,v))|Csct(u,v)∈ Dsct(u,v)},and the spanning t-wide diameter of G,Dsct(G)=max{dsct(u,v)|u,v ∈ V(G)}.In particular,the spanning wide diameter of G is Dsck(G),where κ is the connectivity of G.In the paper we provide the upper and lower bounds of the spanning wide diameter of a graph,and show that the bounds are best possible.We also determine the exact values of wide diameters of some well known graphs including Harary graphs and generalized Petersen graphs et al..
万方数据
