一类新的等可分树和化学树

设T是一个n阶树,e是它的一条边.用n1(e T)和n2(e T)分别表示树T中位于边e两侧的顶点的个数;n1(e T)+n2(e T)=n.设T和T′都是n阶树,e为T的一条边,f为T′的一条边,且n1(e T)=n1(f T′)或者n1(e T)=n2(f T′),则称e和f是等可分的边;如果能适当排列T的边e1,e2,…,en-1和T′的边e1′,e2′,…,en-′1,使得ei和ei′(i=1,2,…,n-1)都是等可分边,则称T和T′是等可分的树.等可分的化学树具有相同的W iener指数,因而有相似的物理化学性质.I.G u tm an等人给出了一些方法,构造等可分的树和化学树.本文给出了一种方法,构造出了一类新的等可分树和化学树.

A New Family of Equiseparable Chemical Trees

Let T be a tree of order n and e its edge.By n_1(e|T) and n_2(e|T) denote the number of vertices of T lying on the two sides of the edge e;n_1(e|T)+n_2(e|T)=n.Let T and T′ be two trees of order n,e is an edge of T and f is an edge of T′.Then e and f are said to be equiseparable if either n_1(e|T)=n_1(f|T′) or n_1(e|T)=n_2(f|T′);and if their edges e_1,e_2,…,e_(n-1) and e~′_1,e~′_2,…,e~′_(n-1) can be labelled so that e_i and e~′_i are equiseparable for all i=1,2,…,n-1,then T and T′ are said to be equiseparable trees.Equiseparable chemical trees have very similar physico-chemical properties since their Wiener indices are equal.Some manners for constructing equiseparable chemical trees were given in the earlier works 1,7,8].In this paper,a new faimly of equiseparable chemical trees is constructed.