Arithmetic Progression Graphs
Universal Journal of Applied Mathematics(2014)
摘要
In this paper we study the problem of labeling the edges of a graph with positive integers such that the sequence of the sums of incident edges of each vertex makes a nite arithmetic progression. We give conditions for paths, cycles, and bipartite graphs to have such a labeling. We then address the opposite problem of nding an edge labeled graph for a given nite arithmetic progression. We use a constructive procedure to fully characterize those nite arithmetic progressions that have rep- resentations as edge labeled graphs. Then by presenting a pseudo polynomial-time algorithm, we address a more general problem of nding edge labels for a graph
更多查看译文
关键词
up to eight vertices,when the vertex labels are given. finally,arithmetic progression,that accept such a labeling by using a simple algorithm that detects a valid edge labeling. key words: graph labeling,graph algorithm,we count the connected graphs,graph labeling
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络