On Properties Of BC Trees

In this paper, we study the properties of BC tree, give out the enumeration of sub BC tree and properties of some kinds of special BC tree; we propose the concepts of Wiener-1, Wiener-2 index and Wiener-1, Wiener-2 distance, and give out its properties on the tree and the BC tree respectively.Firstly, we give out the enumeration of sub BC trees of star BC tree and path BC tree; we analysis the enumeration of sub BC trees passing through any given vertex of path BC tree; contrast the concepts of star BC tree and acceptable subtree residual configuration, we propose the concepts of k extended star BC tree with n-1 branches and acceptable sub BC tree residual configuration, we give out the number of sub BC trees, acceptable sub BC tree residual configuration, sub BC trees relating with original leaf, sub BC trees relating with every layer as well.Combining the concepts of caterpillar tree and BC tree, we give out the concept of caterpillar BC tree, and we study the number of sub BC trees, sub BC trees relating with original leaf, sub BC trees relating with every zone, and give out two special properties of caterpillar BC tree: one property is related with the diameter and the other is the relationship between the number of sub BC trees containing the ends of diameter and the symmetric zone.Corresponding to the concept of Wiener index, In the last of the paper, we propose the concepts of Wiener-1, Wiener-2 index and Wiener-1, Wiener-2 distance, and give out their properties on the tree, next, we give out the realationship between Wiener-1 index and Wiener-2 index of general BC tree,star BC tree,path BC tree,k extended star BC tree,caterpillar BC tree.