序贯可加图的结构

给定一个(p,q)图G和一个正整数k，G的一个k序贯可加性编码是不同的数k,k+1,…,k+p+q-1到G的p+q个元素的一种分配，使得G的每一边e=uv得到分配给顶点u和v的数值之和。若图的元素容许有这样的一种分配，则称该图是一个k序贯可加图。该文将给出序贯可加图的若干结构性质，并构造一个k序贯可加图的无限簇。 

Structare of Sequentially Additive Graphs

Given a (p,q) graph G and positive integer k, an k sequentially additive numbering of G is an assignment of distinct numbers k,k+1,…,k+p+q-1,  to the p+q elements of G such that every edge uv of G receives the sum  of the numbers assigned to the vertices u and v. A graph which admits such an assignment to its  elements is called an k sequentially additive graph. In this paper, the authors give some  structural properties on sequentially additive graph, and a construction of inf inite families of k sequentially additive graphs.