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

Abstract

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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.

How to cite

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Jorge 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

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  1. [1] J.L. Arocha, Anticadenas en conjuntos ordenados, An. Inst. Mat. Univ. Nac. Autónoma México 27 (1987) 1-21. 
  2. [2] C. Berge, Graphs and Hypergraphs (North-Holland, London, 1973). 
  3. [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. [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. [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. [6] C.D. Godsil, Algebraic Combinatorics (Chapman and Hall, New York, 1993). 
  7. [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. [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. [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. [10] N.N. Lebedev, Special Functions and their Applications (Dover, New York, 1972). 
  11. [11] L. Lovász, Combinatorial Problems and Exercises (North-Holland, Amsterdam, 1979). 
  12. [12] O. Ore, Theory of Graphs (Amer. Math. Soc., Providence, 1962). Zbl0105.35401

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