具有完美匹配且直径不大于7的强优美树  

Strongly Graceful Trees with Perfect Matchings and Diameters not Greater than 7

作　　者：陶海霞[1] 姚兵[1] 周向前[1] 

机构地区：[1]西北师范大学数学与信息科学学院,兰州730070

出　　处：《河南师范大学学报（自然科学版）》2012年第1期7-10,共4页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金(61163054;61163037)

摘　　要：一棵具有n个顶点且有完美匹配M的树T,若有一个优美标号f使得对T的每条边uv∈M都有f(u)+f(v)=n-1,则称树T是强优美的.证明所有直径不大于7且有完美匹配的树都是强优美的,并给出了一种构造大的强优美树的方法.A Tree T with n vertices and a perfect matching M is strongly graceful if it has a graceful labeling f such that f（u）＋f（v）=n-1 hold for all edges uv∈M.This research shows that all trees with diameter not greater than seven and perfect matchings are strongly graceful,and furthermore gives a constructive methods for constructing large scale of strongly graceful trees.

关 键 词：树 强优美标号 完美匹配 

分 类 号：O157.5[理学—数学]