Closed formulas for the numbers of small independent sets and matchings and an extremal problem for trees

Discrete Applied Mathematics

Volumn 130, Issue 3, 2003, Pages 503-512

  Delorme, Charles ^a   Favaron, Odile ^a   Rautenbach, Dieter ^b  

^a UFR 919 Laboratoire d'Informatique Pour la Mécanique et les Sciences de l'Ingénieur   (France)

^b UNIVERSITY OF BONN   (Germany)

Author keywords

Degree sequence; Independent set; Kruskal's algorithm; Matching; Tree

Indexed keywords

PROBLEM SOLVING; SET THEORY; THEOREM PROVING;

MATCHINGS;

TREES (MATHEMATICS);

EID: 0042388706     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0166-218X(03)00328-7     Document Type: Article

References (16)

1. Beezer R.A., Farrell E.J., Riegsecker J., Smith B. Graphs with a minimum number of pairs of independent edges. I. matching polynomials Bull. Inst. Combin. Appl. 18:1996;17-32.
2. Bollobás B., Erdos P. Graphs of extremal weights. Ars Combin. 50:1998;225-233.
3. Bollobás B., Erdos P., Sarkar A. Extremal graphs for weights. Discrete Math. 200:1999;5-19.
4. Constantine G.M., Farrell E.J., Guo J.M. On matching coefficients. Discrete Math. 89:1991;203-210.
5. Delorme C., Favaron O., Rautenbach D. On the Randić index. Discrete Math. 257:2002;29-38.
6. Farrell E.J. An introduction to matching polynomials. J. Combin. Theory Ser. B. 27:1979;75-86.
7. M. Fischermann, A. Hoffmann, D. Rautenbach, L. Volkmann, A linear-programming approach to the generalized Randić index, Discrete Appl. Math. 128 (2003) 375-385.
8. M. Fischermann, D. Rautenbach, L. Volkmann, A note on the number of matchings and independent sets in trees, Manuscript, 2001.
9. Godsil C.D., Gutman I. On the theory of the matching polynomial. J. Graph Theory. 5:1981;137-144.
10. Gutman I. The matching polynomial. MATCH - Commun. Math. Comput. Chem. 6:1979;75-91.
11. Gutman I. Numbers of independent vertex and edge sets of a graph. some analogies Graph Theory Notes New York. 22:1992;18-22.
12. Gutman I. Some relations for the independence and matching polynomials and their chemical applications. Bull. Acad. Serbe Sci. Arts. 105:1992;39-49.
13. Hosoya H. Topological index. A newly proposed quantity characterizing the topological nature of structural isomers of saturated hydrocarbons. Bull. Chem. Soc. Jpn. 44:1971;2332-2339.
14. Kruskal J.B. On the shortest spanning subtree of a graph and the traveling Salesman problem. Proc. Amer. Math. Soc. 7:1956;48-50.
15. Lovász L., Plummer M.D. Matching theory. Ann. Discrete Math. 29:1986.
16. Merrifield R.E., Simmons H.E. Topological Methods in Chemistry. 1989;Wiley, New York.