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四类图完美匹配的计数公式 被引量：6

Counting formulas of the number of perfect matchings for four types of graphs
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摘要 用划分,求和,再递推的方法给出了四类图完美匹配数目的显式表达式.所给方法可以计算出许多二分图所有完美匹配的数目. By applying differentiation, summation and re - recursion calculation, several counting formulas of the perfect matchings for four specific types of graphs are given. Many bipartite graphs of the number of all perfect matchings can be calculated by the method presented in this paper.
作者 唐保祥 任韩
机构地区 天水师范学院数学与统计学院 华东师范大学数学系
出处 《福州大学学报（自然科学版）》 CAS CSCD 北大核心 2012年第4期437-440,共4页 Journal of Fuzhou University(Natural Science Edition)
基金 国家自然科学基金资助项目(11171114)
关键词 图 完美匹配 线性递推式 特征方程 graph perfect matching linear recurrence relation characteristic equation
分类号 O157.5 [理学—基础数学]
  • 相关文献

参考文献19

  • 1Bondy J A, Murty U S R. Graph theory with applications[M]. New York: MacMilan Press, 1976.
  • 2Hall G G. A graphic model of a class of molecules[J]. Int J Math Edu Sci, 1973(4) : 233 -240.
  • 3Pauling L. The nature of chemical bond, Comell[M]. New York: Ithaca Univ Press, 1939.
  • 4Cyvin S J, Gutman I. Kekul6 structures in Benzennoid hydrocarbons [ M ]. Berlin: Springer Press, 1988.
  • 5Kasteleyn P W. Graph theory and crystal physics [ M ]//Harary F. Graph Theory and Theoretical Physics. London: Academic Press, 1967 : 43 - 110.
  • 6Lov6sz L, Plummer M. Matching theory[ M]. New York: North -Holland Press, 1986.
  • 7Ciucu M. Enumeration of perfect matchings in graphs with reflective symmetry[J]. J Combin Theory: A, 1997, 77:87 -97.
  • 8Fischer I, Little C H C. Even circuits of prescribed clockwise parity[J/OL]. Electronic Journal of Combinatorics, 2003 [2010 -04 -20]. http://www, emisamsorg/journals/EJC/Volume 10/PDF/Vloilr45. pdf.
  • 9Jockusch W. Perfect mathings and perfect squares [ J ]. J Combin Theory: A, 1994, 67 : 100 - 115.
  • 10Kasteleyn P W. The number of dimmer on a quadratic lattice[J]. Physica, 1961, 27 : 1 209 - 1 225.

二级参考文献31

  • 1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. 被引量：29
  • 2Hall G G.A graphic model of a class of molecules[J].Int J Math Edu Sci,1973,4:233-240.
  • 3Pauling L.The Nature of Chemical Bond,Cornell[M].Ithaca:Univ Press,1939.
  • 4Cyvin S J,Gutman I.Kekulé structures in Benzennoid hydrocarbons[M].Berlin:Springer Press,1988.
  • 5Kasteleyn P W.Graph theory and crystal physics[M] // Harary F.Graph Theory and Theoretical Physics.London:Academic Press,1967:43-110.
  • 6Lovász L,Plummer M.Matching Theory[M].New York:North-Holland Press,1986.
  • 7Ciucu M.Enumeration of perfect matchings in graphs with reflective symmetry[J].J Combin Theory Ser A,1997,77:87-97.
  • 8Fischer I,Little C H C.Even circuits of prescribed clockwise parity[J/OL].Electro J Combin,2003,10[2010-04-20].http://www.emis.ams.org/journals/EJC/Volume-10/PDF/V1oi1r45.pdf.
  • 9Jockusch W.Perfect mathings and perfect squares[J].J Combin Theory Ser A,1994,67:100-115.
  • 10Brightwell G R,Winkler P,Hard C,et al.Adventures at the interface of combinatories and statistical physics[J].ICM,2002,III:605-624.

共引文献52

同被引文献63

  • 1任韩,镡松龄,马登举.稠密图的三角剖分嵌入(英文)[J].昆明理工大学学报（自然科学版）,2012,37(2):83-87. 被引量：3
  • 2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. 被引量：29
  • 3Kasteleyn P W. Graph Theory and Crystal Physics[C]//Harary F. Graph Theory and Theoretical Physics, London: Aca demic Press, 1967 : 43-110.
  • 4Hall G G. A Graphic Model of a Class of Molecules[J]. Int J Math Edu Sci Techno1,1973,4(3) :233-240.
  • 5Cyvin S J ,Gutman I. Kekul6 Structures in Benzennoid Hydrocarbons[M]. Berlin:Springer Press, 1988.
  • 6Ciucu M. Enumeration of Perfect Matehings in Graphs with Reflective Symmetry[J]. J Combin Theory Ser A, 1997,77 87-97.
  • 7Fischer I, Little C H C. Even Circuits of Prescribed Clockwise Parity[J/OL]. Electro J Combin, 2003,10:1-20[2010-04- 20]. http://www, emis. ams. org/journals/EJC/Volume_10/PDF/Vloilr45, pdf.
  • 8Jockusch W. Perfect Mathings and Perfect Squares[J]. J Combin Theory Ser A ,1994,67:100-115.
  • 9Kasteleyn P W. Dimmer Statistics and Phase Transition[J]. Journal of Mathematical Physics, 1963,4:287-293.
  • 10Lovdsz L,Plummer M. Matching Theory[M]. New York:North-Holland Press, 1986.

引证文献6

二级引证文献19

福州大学学报（自然科学版）
2012年 第4期

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