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《山东大学学报(理学版)》 ›› 2023, Vol. 58 ›› Issue (12): 140-150.doi: 10.6040/j.issn.1671-9352.0.2022.434

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基于图运算下的控制熵

汲颖1,2(),邓波1,2,赵海兴1,2,3,*(),唐彦龙2,3   

  1. 1. 青海师范大学数学与统计学院, 青海 西宁 810008
    2. 藏语智能信息处理及应用国家重点实验室, 青海 西宁 810008
    3. 青海师范大学计算机学院, 青海 西宁 810008
  • 收稿日期:2022-08-19 出版日期:2023-12-20 发布日期:2023-12-19
  • 通讯作者: 赵海兴 E-mail:jiying197@163.com;h.x.zhao@163.com
  • 作者简介:汲颖(1997—)，女，硕士研究生，研究方向为图论及其应用. E-mail：jiying197@163.com
  • 基金资助:
    111引智计划项目(D20035);国家重点研发计划项目(2020YFC1523300);青海省科技厅资助项目(2022-ZJ-T02)

Domination entropy based on graph operations

Ying JI1,2(),Bo DENG1,2,Haixing ZHAO1,2,3,*(),Yanlong TANG2,3   

  1. 1. College of Mathematics and Statistics, Qinghai Normal University, Xining 810008, Qinghai, China
    2. State Key Laboratory of Tibetan Intelligent Information Processing and Application, Xining 810008, Qinghai, China
    3. College of Computer, Qinghai Normal University, Xining 810008, Qinghai, China
  • Received:2022-08-19 Online:2023-12-20 Published:2023-12-19
  • Contact: Haixing ZHAO E-mail:jiying197@163.com;h.x.zhao@163.com

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摘要：

图不变量广泛应用于构建基于熵的度量以表征复杂网络的结构。特别地, 基于控制集的图熵常应用于刻画通信系统的信息量和计算机网络的稳定性。研究完全图、星图、梳状图和友谊图在不交的并、联图、冠积和笛卡尔积4种图运算下基于控制集的图熵计算。

关键词: 图熵, 图运算, 控制多项式, 控制熵

Abstract:

Graph invariants are widely used to construct entropy-based metrics to characterize the structure of complex networks. In particular, graph entropy based on dominating sets is often applied to characterize the amount of information in communication systems and the stability of computer networks. Graph entropy calculations are studied based on dominating sets under the four operations of graphs. That is the operations of the disjoint union, joining, corona product, and Cartesian product using the complete graph, star graph, comb graph, and friendship graph.

Key words: graph entropy, graph operation, domination polynomial, domination entropy

中图分类号: 

  • O157.5

图1

梳状图En"

图2

友谊图F2、F3和F4"

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