直径为5的一类树的拟序

Quasi-order in a class of trees with diameter five

本文研究了直径为5的一类特殊树的拟序和能量.在直径为5的树中,分别固定树的两个中心点的度,以及到这两个中心点构成的点集的最短距离为2的悬挂点的总数;使与同一中心点邻接的任意两个非中心点各自邻接的悬挂点数最多相差1,且其中一个中心点的任意非中心邻点至多是二度点.本文主要研究这类树的悬挂点的分配导致拟序的变化,进而导致能量大小的变化,得到在阶为n且直径为5,中心点的度为SH和t+1的树T′中,当p≥q+2,q=1时,到两个中心点构成的点集的最短距离为2的所有悬挂点分布越均匀,拟序越优。此结论有助于在直径为5的树中确定具有极大能量的图的结构.

This paper studies the quasi-order and energy in a class of special trees with diameter five.In a tree with diameter five,remain the degrees of two center vertices,respectively.As well as fix the total number of pendent vertices with shortest distance two from the set of two center vertices,so that the difference between the numbers of pendent vertices adjacent to two noncentral vertices that are neighbors of same center vertex is at most one.Moreover,the degrees of any non-central neighbors of one of the center vertices is at most two.The paper mainly studies the variations of quasi-order in the trees discribe above.The variations come with the change of distribution of pendent vertices,and leads to the change of energy.The theorem of the paper is contributed to determine the structure of graph with maximal energy in the tree with diameter five.