数学季刊 ›› 2022, Vol. 37 ›› Issue (4): 380-385.doi: 10.13371/j.cnki.chin.q.j.m.2022.04.005

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哈林图的导出匹配可扩性

  

  1. 1. School of Mathematics and Statistics, Pingdingshan University, Pingdingshan 467000, China; 2. International Joint Laboratory for Multidimensional Topology and Carcinogenic Characteristics Analysis of Atmospheric Particulate Matter PM2.5, Pingdingshan 467000, China; 3. School of Software, Pingdingshan University, Pingdingshan 467000, China
  • 收稿日期:2022-05-20 出版日期:2022-12-30 发布日期:2022-12-30
  • 通讯作者: HUI Zhi-hao (1980-), male, native of Nanyang, Henan, associate professor of Pingdingshan University, engages in graph theory and network optimization; E-mail:hzh@pdsu.edu.cn
  • 作者简介: ZHANG Qing-nan (2000-), female, native of Kaifeng, Henan, undergraduate students of Pingdingshan University, engages in graph calculation; HUI Zhi-hao (1980-), male, native of Nanyang, Henan, associate professor of Pingdingshan University, engages in graph theory and network optimization; YANG Yu (1983-), male, native of Nanyang, Henan, associate professor of Pingdingshan University, engages in graph computing and big data technology; WANG An (1983-), male, native of Kaifeng, Henan, lecturer of Pingdingshan University, engages in grey systems and machine learning.
  • 基金资助:
     Supported by the National Natural Science Foundation of China (Grant Nos. 61702291, 11801371); Key Research Project in Universities of Henan Province (Grant No. 21B110004). 

Induced Matching-Extendability of Halin Graphs

  1. 1. School of Mathematics and Statistics, Pingdingshan University, Pingdingshan 467000, China; 2. International Joint Laboratory for Multidimensional Topology and Carcinogenic Characteristics Analysis of Atmospheric Particulate Matter PM2.5, Pingdingshan 467000, China; 3. School of Software, Pingdingshan University, Pingdingshan 467000, China
  • Received:2022-05-20 Online:2022-12-30 Published:2022-12-30
  • Contact: HUI Zhi-hao (1980-), male, native of Nanyang, Henan, associate professor of Pingdingshan University, engages in graph theory and network optimization; E-mail:hzh@pdsu.edu.cn
  • About author: ZHANG Qing-nan (2000-), female, native of Kaifeng, Henan, undergraduate students of Pingdingshan University, engages in graph calculation; HUI Zhi-hao (1980-), male, native of Nanyang, Henan, associate professor of Pingdingshan University, engages in graph theory and network optimization; YANG Yu (1983-), male, native of Nanyang, Henan, associate professor of Pingdingshan University, engages in graph computing and big data technology; WANG An (1983-), male, native of Kaifeng, Henan, lecturer of Pingdingshan University, engages in grey systems and machine learning.
  • Supported by:
     Supported by the National Natural Science Foundation of China (Grant Nos. 61702291, 11801371); Key Research Project in Universities of Henan Province (Grant No. 21B110004). 

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摘要：  Let G be a connected graph having a perfect matching. The graph G is said to be induced matching (IM) extendable if every induced matching M of G is contained in a perfect matching of G. In this paper, we show that Halin graph G =T ∪C is IMextendable if and only if its characteristic tree T is isomorphic to K1,3, K1,5, K1,7 or S2,2.

关键词: Halin graph, Perfect matching, Induced matching, Induced matching extendable

Abstract:  Let G be a connected graph having a perfect matching. The graph G is said to be induced matching (IM) extendable if every induced matching M of G is contained in a perfect matching of G. In this paper, we show that Halin graph G =T ∪C is IMextendable if and only if its characteristic tree T is isomorphic to K1,3, K1,5, K1,7 or S2,2.

Key words: Halin graph, Perfect matching, Induced matching, Induced matching extendable

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