文章摘要
扇轮及其联图的点可约全标号
Vertex Reducible Total Labeling of the fan wheel and its associated graph
投稿时间:2023-12-26  修订日期:2024-01-28
DOI:
中文关键词: 联图  点可约全标号  VRTL图  递归搜索算法  
英文关键词: Join graph  Vertex Reducible Total Labeling  VRTL diagram  Recursive search algorithm  
基金项目:国家自然科学基金(11961041;62262038);甘肃省媒体融合技术与传播重点实验室(21ZD8RA008),
作者单位
李敬文 兰州交通大学 电子与信息工程学院 
高鑫* 兰州交通大学 电子与信息工程学院 
王江 兰州交通大学 电子与信息工程学院 
黄聪 兰州交通大学 电子与信息工程学院 
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中文摘要:
      对于一个无向连通图,其中p为点数,q为边数,若存在一个单一映射,使得对于图中所有度相同的点及其关联边的标号和都为常数,则称该映射关系f为G的点可约全标号(Vertex Reducible Total Labeling,简称VRTL)。本文通过优化点可约全标号的传统算法,针对点可约全标号的解空间进行递归搜索,通过总结扇图、轮图及其联图在有限点内的标号规律,给出针对该类图形的全标号定理并给出证明。
英文摘要:
      For an undirected connected graph , where p is the number of points and q is the number of edges, if there is a single mapping ,so that the sum of labels for all points with the same degree and their associated edges in the graph is constant, then the mapping relationship is called Vertex Reduced Total Labeling (VRTL). This article optimizes the traditional algorithm of point reducible total labeling and recursively searches the solution space of point reducible total labeling. By summarizing the labeling laws of fan graphs, wheel graphs, and their associated graphs within finite points, a total labeling theorem for this type of graph is presented and proved.
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