一类整和图  

A Family of Integral Sum Graphs

作　　者：高敬振[1] 李婧梓[1] 

机构地区：[1]山东师范大学数学科学学院,山东省济南市250014

出　　处：《曲阜师范大学学报（自然科学版）》2007年第3期9-11,共3页Journal of Qufu Normal University(Natural Science)

基　　金：山东省高等学校教学改革立项基金(B05038)

摘　　要：一个图G称为整和图,若它有一组互异的整数标号f,使得G中任意两个不同点u、v,uv是G中的一条边当且仅当f(u)+f(v)=f(w)(其中w是G中的一点).一个图称为星和图,若它不含与其它顶点都邻接的顶点且有一组整和标号含有负标号和唯一绝对值最大点.广义星是将星的每一边都扩展为一条路的图.粘合是将两个图G1、G2中的各一个点r1、r2合为一个点r的运算.该文考虑了一类新图——星和图与广义星的粘合图,证明了它的整和性.A graph G is said to be an integral sum graph if its points can be given a labeling f with distinct integers,such that for any two distinct points u,v∈G, uv is an edge of G if and only if f（u）＋f（v）= f（w） for some point w of G. A graph is said to be a （ ＊ ）-sum graph if it has no point which is adjacent to other points of the graph, and it has an integral sum labeling which has a negative integral label and a sole point which absolute value is maximum. A generalized star is obtained from a star by extending each edge to a path. In this paper, a new family of graphs-（ ＊ ）-sum graph identified with a generalized star-is discussed and proved to be integral sum graphs.

关 键 词：整和图 粘合 星和图 广义星 

分 类 号：O157.5[理学—数学]