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..
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