广义Corona积图的度量维研究

发布时间：2018-06-14 00:52

本文选题：Corona积 + 分辨集　；参考：《应用数学学报》2017年06期

【摘要】：图的分辨集和度量维问题是与网络(顶点)信息识别有关的一类涉及包括机器人导航和网络入侵者定位问题在内的多个实际研究邻域的重要组合优化问题.一些大型网络可以看作是通过图的乘积运算而得到.本文定义了广义Corona积图.研究并刻画了积图分辨集和基的一般构成特性,得出了积图度量维的界.基于子图顶点距离划分,给出了积图度量维的一般计算公式;建立了寻找积图基的算法和计算积图度量维的0-1整数规划模型.作为应用,计算了一些特殊广义Corona积图的度量维.
[Abstract]:The problem of discernibility set and measurement dimension of graph is a kind of important combinatorial optimization problem related to network (vertex) information recognition which involves many practical neighborhood problems including robot navigation and network intruder location. Some large networks can be regarded as the product of graphs. In this paper, the generalized Corona product graph is defined. This paper studies and characterizes the general construction properties of the discernibility set and the basis of the product graph, and obtains the bounds of the metric dimension of the product graph. Based on the subgraph vertex distance partition, the general calculation formula of product graph metric dimension is given, and the algorithm for finding the basis of product graph and the 0-1 integer programming model for calculating product graph metric dimension are established. As an application, the metric dimensions of some special generalized Corona product graphs are calculated.
【作者单位】：山西财经大学应用数学学院;山西财经大学统计学院;
【基金】：国家自然科学基金(11626149)资助项目
【分类号】：O157.5

【相似文献】