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TANG Baoxiang, REN Han. A Recursive Method for Perfect Matching Number Classified with Saturation of a Certain Vertex[J]. Journal of South China Normal University (Natural Science Edition), 2019, 51(5): 110-114. DOI: 10.6054/j.jscnun.2019092
Citation: TANG Baoxiang, REN Han. A Recursive Method for Perfect Matching Number Classified with Saturation of a Certain Vertex[J]. Journal of South China Normal University (Natural Science Edition), 2019, 51(5): 110-114. DOI: 10.6054/j.jscnun.2019092

A Recursive Method for Perfect Matching Number Classified with Saturation of a Certain Vertex

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  • Received Date: October 30, 2018
  • Available Online: March 08, 2021
  • Two new graphs 2-2nK5 and 2-nZ5 are constructed. Using the nested recursive method, two recursive relations of the perfect matching numbers of graphs 2-2nK5 and 2-nZ5 are obtained, and then the two recursive general solutions are solved. Thus, the formula for calculating the perfect matching number of these two types of graphs is obtained.
  • [1]
    LOVÁSZ L, PLUMMER M. Matching theory[M]. New York:North-Holland Press, 1986.
    [2]
    ZHANG H P. The connectivity of Z-transformation graphs of perfect matchings of polyominoes[J]. Discrete Mathematics, 1996, 158:257-272. doi: 10.1016/0012-365X(95)00048-2
    [3]
    ZHANG H P, ZHANG F J. Perfect matchings of polyomino graphs[J]. Graphs and Combinatorics, 1997, 13:259-304. doi: 10.1007-s00373-004-0593-9/
    [4]
    LI S L, YAN W G. The matching energy of graphs with given parameters[J]. Discrete Applied Mathematics, 2014, 162:415-420. doi: 10.1016/j.dam.2013.09.014
    [5]
    DONG F M, YAN W G, ZHANG F J. On the number of perfect matchings of line graphs[J]. Discrete Applied Mathematics, 2013, 161:794-801. doi: 10.1016/j.dam.2012.10.032
    [6]
    YAN W G, ZHANG F J. A quadratic identity for the number of perfect matchings of plane graphs[J]. Theoretical Computer Science, 2008, 409:405-410. doi: 10.1016/j.tcs.2008.08.032
    [7]
    CHANG A, TIAN F, YU A M. On the index of bicyclic graphs with perfect matchings[J]. Discrete Mathematics, 2004, 283:51-59. doi: 10.1016/j.disc.2004.02.005
    [8]
    CHANG A, SHIU W C. On the kth eigenvalues of trees with perfect matchings[J]. Discrete Mathematics and Theoretical Computer Science, 2007, 9(1):321-332
    [9]
    林泓, 林晓霞.若干四角系统完美匹配数的计算[J].福州大学学报(自然科学版), 2005, 33(6):704-710. doi: 10.3969/j.issn.1000-2243.2005.06.003

    LIN H, LIN X X. Enumeration of perfect matchings in some type polyminoes[J]. Journal of Fuzhou University(Natural Sciences Edition), 2005, 33(6):704-710. doi: 10.3969/j.issn.1000-2243.2005.06.003
    [10]
    唐保祥, 李刚, 任韩. 3类图完美匹配的数目[J].浙江大学学报(理学版), 2011, 38(4):16-19. http://d.old.wanfangdata.com.cn/Periodical/zjdxxb201104005

    TANG B X, LI G, REN H. The number of perfect mat-ching for three specific types of graphs[J]. Journal of Zhejiang University(Science Edition), 2011, 38(4):16-19. http://d.old.wanfangdata.com.cn/Periodical/zjdxxb201104005
    [11]
    唐保祥, 任韩. 4类图完美匹配数目的递推求法[J].数学杂志, 2015, 353(2):626-634. http://d.old.wanfangdata.com.cn/Periodical/hnsfdx201401004

    TANG B X, REN H. Recursive method for finding the number of perfect matchings of the four types of graphs[J]. Journal of Mathematics, 2015, 353(2):626-634. http://d.old.wanfangdata.com.cn/Periodical/hnsfdx201401004
    [12]
    唐保祥, 任韩. 3类特殊图完美对集数的计算[J].南开大学学报(自然科学版), 2014, 47(5):11-16. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=nkdx201405002

    TANG B X, REN H. The enumeration of perfect mat-chings in three types of special graphs[J]. Journal of Nankai University(Science Edition), 2014, 47(5):11-16. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=nkdx201405002
    [13]
    唐保祥, 任韩. 4类图完美匹配的计数[J].武汉大学学报(理学版), 2012, 58(5):441-446. http://d.old.wanfangdata.com.cn/Periodical/whdxxb-zr201205015

    TANG B X, REN H. The number of perfect matchings in four types of graphs[J]. Journal of Wuhan University(Natural Science Edition), 2012, 58(5):441-446. http://d.old.wanfangdata.com.cn/Periodical/whdxxb-zr201205015
    [14]
    唐保祥, 任韩.两类图完美匹配的计数公式[J].吉林大学学报(理学版), 2016, 54(4):790-792. http://d.old.wanfangdata.com.cn/Periodical/jldxzrkxxb201604021

    TANG B X, REN H. Counting formulas of the number of perfect matchings of the two types of graphs[J]. Journal of Jilin University(Science Edition), 2016, 54(4):790-792. http://d.old.wanfangdata.com.cn/Periodical/jldxzrkxxb201604021
    [15]
    唐保祥, 任韩. 2类图完美匹配数目的解析式[J].中山大学学报(自然科学版), 2016, 55(4):15-17. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=zsdxxb201604003

    TANG B X, REN H. The analytic formula of the number of perfect matchings of two types of graphs[J]. Acta Scientiarum Naturalium Universitatis Sunyatseni, 2016, 55(4):15-17. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=zsdxxb201604003
    [16]
    唐保祥, 任韩. 2类特殊图中的完美匹配数[J].浙江大学学报(理学版), 2017, 44(3):266-269. http://d.old.wanfangdata.com.cn/Periodical/zjdxxb201703003

    TANG B X, REN H. The number of perfect matchings in two types of particular graphs[J]. Journal of Zhejiang University(Science Edition), 2017, 44(3):266-269. http://d.old.wanfangdata.com.cn/Periodical/zjdxxb201703003
    [17]
    唐保祥, 任韩. 4类图完美匹配数目的递推求法[J].数学杂志, 2015, 353(2):626-634. http://d.old.wanfangdata.com.cn/Periodical/hnsfdx201401004

    TANG B X, REN H. Recursive method for finding the number of perfect matchings of the four types of graphs[J]. Journal of Mathematics, 2015, 353(2):626-634. http://d.old.wanfangdata.com.cn/Periodical/hnsfdx201401004
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