按匹配顶点分类的完美匹配数递推求法
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摘要
先把图2-nZ6,2-nXT3的完美匹配按匹配某个顶点进行分类,求出一组相互联系的完美匹配数递推关系式,再由这组递推关系式给出这两类图的完美匹配数计算公式.
Firstly,the perfect matching of the graph 2-nZ6,2-nXT3 was classified by matching a certain vertex,and a recursive relation of a set of perfect matching numbers was obtained.Then the formulas for calculating the perfect matching numbers of two types of graphs were given by these recursive relations.
Firstly,the perfect matching of the graph 2-nZ6,2-nXT3 was classified by matching a certain vertex,and a recursive relation of a set of perfect matching numbers was obtained.Then the formulas for calculating the perfect matching numbers of two types of graphs were given by these recursive relations.
引文
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[2]ZHANG Heping.The Connectivity of Z-Transformation Graphs of Perfect Matchings of Polyominoes[J].Discrete Math,1996,158(1/2/3):257-272.
[3]ZHANG Heping,ZHANG Fuji.Perfect Matchings of Polyomino Graphs[J].Graphs Combin,1997,13(3):295-304.
[4]LI Shuli,YAN Weigen.The Matching Energy of Graphs with Given Parameters[J].Discrete Appl Math,2014,162:415-420.
[5]DONG Fengming,YAN Weigen,ZHANG Fuji.On the Number of Perfect Matchings of Line Graphs[J].Discrete Appl Math,2013,161(6):794-801.
[6]YAN Weigen,ZHANG Fuji.A Quadratic Identity for the Number of Perfect Matchings of Plane Graphs[J].Theoret Comput Sci,2008,409(3):405-410.
[7]CHANG An,TIAN Feng,YU Aimei.On the Index of Bicyclic Graphs with Perfect Matchings[J].Discrete Math,2004,283(1/2/3):51-59.
[8]CHANG An,SHIU W C.On the kth Eigenvalues of Trees with Perfect Matchings[J].Discrete Math Theoret Comput Sci,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.(LIN Hong,LIN Xiaoxia.Enumeration of Perfect Matchings in Some Type Polyminoes[J].Journal of Fuzhou University(Natural Sciences Edition),2005,33(6):704-710.)
[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):387-390.(TANG Baoxiang,LI Gang,REN Han.The Number of Perfect Matching for Three Specific Types of Graphs[J].Journal of Zhejiang University(Science Edition),2011,38(4):387-390.)
[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,2015,35(3):626-634.(TANG Baoxiang,REN Han.Recursive Method for Finding the Number of Perfect Matchings of the Four Types of Graphs[J].Journal of Mathematics,2015,35(3):626-634.)
[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.(TANG Baoxiang,REN Han.The Enumeration of Perfect Matchings in Three Types of Special Graphs[J].Acta Scientiarum Naturalium Universitatis Nankaiensis,2014,47(5):11-16.)
[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.(TANG Baoxiang,REN Han.The Number of Perfect Matchings for Four Types of Graphs[J].Journal of Wuhan University(Natural Science Edition),2012,58(5):441-446.)
[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.(TANG Baoxiang,REN Han.Counting Formulas of Perfect Matchings of Two Types of Graphs[J].Journal of Jilin University(Science Edition),2016,54(4):790-792.)
[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.(TANG Baoxiang,REN Han.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.)
[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.(TANG Baoxiang,REN Han.The Number of Perfect Matchings in Two Types of Particular Graphs[J].Journal of Zhejiang University(Science Edition),2017,44(3):266-269.)
[2]ZHANG Heping.The Connectivity of Z-Transformation Graphs of Perfect Matchings of Polyominoes[J].Discrete Math,1996,158(1/2/3):257-272.
[3]ZHANG Heping,ZHANG Fuji.Perfect Matchings of Polyomino Graphs[J].Graphs Combin,1997,13(3):295-304.
[4]LI Shuli,YAN Weigen.The Matching Energy of Graphs with Given Parameters[J].Discrete Appl Math,2014,162:415-420.
[5]DONG Fengming,YAN Weigen,ZHANG Fuji.On the Number of Perfect Matchings of Line Graphs[J].Discrete Appl Math,2013,161(6):794-801.
[6]YAN Weigen,ZHANG Fuji.A Quadratic Identity for the Number of Perfect Matchings of Plane Graphs[J].Theoret Comput Sci,2008,409(3):405-410.
[7]CHANG An,TIAN Feng,YU Aimei.On the Index of Bicyclic Graphs with Perfect Matchings[J].Discrete Math,2004,283(1/2/3):51-59.
[8]CHANG An,SHIU W C.On the kth Eigenvalues of Trees with Perfect Matchings[J].Discrete Math Theoret Comput Sci,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.(LIN Hong,LIN Xiaoxia.Enumeration of Perfect Matchings in Some Type Polyminoes[J].Journal of Fuzhou University(Natural Sciences Edition),2005,33(6):704-710.)
[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):387-390.(TANG Baoxiang,LI Gang,REN Han.The Number of Perfect Matching for Three Specific Types of Graphs[J].Journal of Zhejiang University(Science Edition),2011,38(4):387-390.)
[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,2015,35(3):626-634.(TANG Baoxiang,REN Han.Recursive Method for Finding the Number of Perfect Matchings of the Four Types of Graphs[J].Journal of Mathematics,2015,35(3):626-634.)
[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.(TANG Baoxiang,REN Han.The Enumeration of Perfect Matchings in Three Types of Special Graphs[J].Acta Scientiarum Naturalium Universitatis Nankaiensis,2014,47(5):11-16.)
[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.(TANG Baoxiang,REN Han.The Number of Perfect Matchings for Four Types of Graphs[J].Journal of Wuhan University(Natural Science Edition),2012,58(5):441-446.)
[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.(TANG Baoxiang,REN Han.Counting Formulas of Perfect Matchings of Two Types of Graphs[J].Journal of Jilin University(Science Edition),2016,54(4):790-792.)
[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.(TANG Baoxiang,REN Han.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.)
[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.(TANG Baoxiang,REN Han.The Number of Perfect Matchings in Two Types of Particular Graphs[J].Journal of Zhejiang University(Science Edition),2017,44(3):266-269.)