# Mean value for the matching and dominating polynomial

Jorge Luis Arocha; Bernardo Llano

Discussiones Mathematicae Graph Theory (2000)

- Volume: 20, Issue: 1, page 57-69
- ISSN: 2083-5892

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topJorge Luis Arocha, and Bernardo Llano. "Mean value for the matching and dominating polynomial." Discussiones Mathematicae Graph Theory 20.1 (2000): 57-69. <http://eudml.org/doc/270566>.

@article{JorgeLuisArocha2000,

abstract = {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.},

author = {Jorge Luis Arocha, Bernardo Llano},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {matching; matching polynomial; dominating set; dominating polynomial},

language = {eng},

number = {1},

pages = {57-69},

title = {Mean value for the matching and dominating polynomial},

url = {http://eudml.org/doc/270566},

volume = {20},

year = {2000},

}

TY - JOUR

AU - Jorge Luis Arocha

AU - Bernardo Llano

TI - Mean value for the matching and dominating polynomial

JO - Discussiones Mathematicae Graph Theory

PY - 2000

VL - 20

IS - 1

SP - 57

EP - 69

AB - 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.

LA - eng

KW - matching; matching polynomial; dominating set; dominating polynomial

UR - http://eudml.org/doc/270566

ER -

## References

top- [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. Zbl0335.05131
- [4] M.R. Garey and D.S. Johnson, Computers and Intractability: A Guide to the Theory of NP-completeness (Freeman, New York, 1979). Zbl0411.68039
- [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. Zbl0228.05131
- [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. Zbl0870.05034
- [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). Zbl0105.35401

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