Induced Matching-Extendability of Halin Graphs

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  • 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
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.

Received date: 2022-05-20

  Online published: 2022-12-30

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). 

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.

Cite this article

ZHANG Qing-nan, HUI Zhi-hao, YANG Yu, WANG An, . Induced Matching-Extendability of Halin Graphs[J]. Chinese Quarterly Journal of Mathematics, 2022 , 37(4) : 380 -385 . DOI: 10.13371/j.cnki.chin.q.j.m.2022.04.005

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