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Enumeration of graphs with given weighted number of connected components

송정민
대한수학회 (The Korean Mathematical Society)|2017.11|대한수학회보 (Bulletin of the KMS)|제54권 제6호|pp. 1873-1882

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참고문헌

키워드

generating functions$q$-partite graphs
주제분류수학

초록

We give a generating function for the number of graphs with given numerical properties and prescribed weighted number of connected components. As an application, we give a generating function for the number of $q$-partite graphs of given order, size and number of connected components.

Abstract

We give a generating function for the number of graphs with given numerical properties and prescribed weighted number of connected components. As an application, we give a generating function for the number of $q$-partite graphs of given order, size and number of connected components.

참고문헌 (13)

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  3. F. Harary, "On the number of bi-colored graphs", Pacific J. Math, 8, pp.743~755 (1958)
  4. F. Harary, "Graphical enumeration" (1973), Academic Press
  5. F. Harary, "Enumeration of bicolourable graphs", Canad. J. Math, 15, pp.237~248 (1963)
  6. T. W. Melnyk, "The penetrable sphere and related models of liquid vapour equilibrium", Molecular Physics, 24(4), pp.809~831 (1972)
  7. R. C. Read, "Some enumeration problems in graph theory", Doctor, pp.1958
  8. R. C. Read, "The number of k-colored graphs on labelled nodes", Canad. J. Math, 12, pp.410~414 (1960)
  9. , ~
  10. 송정민, "ENUMERATION OF GRAPHS AND THE CHARACTERISTIC POLYNOMIAL OF THE HYPERPLANE ARRANGEMENTS Jn", 대한수학회지, 54(5), pp.1595~1604 (2017), 대한수학회
  11. 송정민, "On certain hyperplane arrangements and colored graphs", 대한수학회보, 54(2), pp.375~382 (2017), 대한수학회
  12. R. P. Stanley, "Enumerative combinatorics. Vol. 2" (1999), Cambridge University Press
  13. M. Ueno, "Enumeration of bipartite self-complementary graphs", Graphs Combin, 30(2), pp.471~477 (2014)

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