Mean value for the matching and dominating polynomial

• Autorzy: Jorge Luis Arocha , Bernardo Llano
• Języki publikacji: EN

Abstrakty

EN

The mean value of the matching polynomial is computed in the family of all labeled graphs with n vertices. We introduce the dominating polynomial of a graph whose coefficients enumerate the dominating sets for a graph and study some properties of the polynomial. The mean value of this polynomial is determined in a certain special family of bipartite digraphs.

Słowa kluczowe

EN

matching; matching polynomial; dominating set

Kategorie tematyczne

• 05C70: Factorization, matching, partitioning, covering and packing
• 05A15: Exact enumeration problems, generating functions

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2000
• Tom: 20
• Numer: 1
• Strony: 57-69

Daty

wydano

2000

otrzymano

1999-02-03

poprawiono

1999-05-06

Twórcy

autor

Jorge Luis Arocha

• Instituto de Matemáticas, UNAM, Circuito Exterior, Ciudad Universitaria, México, D.F. 04510

autor

Bernardo Llano

• Instituto de Matemáticas, UNAM, Circuito Exterior, Ciudad Universitaria, México, D.F. 04510

Bibliografia

• [1] J.L. Arocha, Anticadenas en conjuntos ordenados, An. Inst. Mat. Univ. Nac. Autónoma México 27 (1987) 1-21.
• [2] C. Berge, Graphs and Hypergraphs (North-Holland, London, 1973).
• [3] E.J. Farrell, An introduction to matching polynomials, J. Combin. Theory (B) 27 (1979) 75-86, doi: 10.1016/0095-8956(79)90070-4.
• [4] M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-completeness (Freeman, New York, 1979).
• [5] C.D. Godsil and I. Gutman, On the theory of the matching polynomial, J. Graph Theory 5 (1981) 137-144, doi: 10.1002/jgt.3190050203.
• [6] C.D. Godsil, Algebraic Combinatorics (Chapman and Hall, New York, 1993).
• [7] O.J. Heilmann and E.H. Lieb, Monomers and dimers, Phys. Rev. Lett. 24 (1970) 1412-1414, doi: 10.1103/PhysRevLett.24.1412.
• [8] O.J. Heilmann and E.H. Lieb, Theory of monomer-dimer systems, Comm. Math. Phys. 25 (1972) 190-232, doi: 10.1007/BF01877590.
• [9] M.A. Henning, O.R. Oellermann and H.C. Swart, The diversity of domination, Discrete Math. 161 (1996) 161-173, doi: 10.1016/0012-365X(95)00074-7.
• [10] N.N. Lebedev, Special Functions and their Applications (Dover, New York, 1972).
• [11] L. Lovász, Combinatorial Problems and Exercises (North-Holland, Amsterdam, 1979).
• [12] O. Ore, Theory of Graphs (Amer. Math. Soc., Providence, 1962).

Identyfikatory

DOI

10.7151/dmgt.1106