Advertisement

Application of the Maximum Real Roots of Matching Polynomial

  • Youfu Qiao
  • Fuqin Zhan
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7030)

Abstract

To discuss the matching uniqueness of the simple undirected graph G. To find the necessary and sufficient conditions for the matching uniqueness of T(a,b,c). Use the maximum real roots, and the properties of matching polynomials to compute. For n ≥ 5, T(1,5,n) and its complement are matching uniqueness if and only if n ≠ 5,8 and 15.

Keywords

Matching polynomial Matching equivalence Matching uniqueness The maximum real roots 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Godsil, C.D.: Algebraic Combinatorics. Chapman and Hall, New York (1993)zbMATHGoogle Scholar
  2. 2.
    Bondy, J.A., Murty, U.S.R.: Graph Theory with Applications. North-Holland, Amsterdam (1976)CrossRefzbMATHGoogle Scholar
  3. 3.
    Ma, H.: Graphs Characterized by the Roots of Matching. Journal of Qufu Normal University (Natural Science) 27(1), 33–36 (2001)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Ma, H.: The Graphs G with \(2<M(G)\leq{\sqrt{2+\sqrt5}}\). Acta Scientiarum Naturalium Universitatis Neimongol 36(5), 485–487 (2005)Google Scholar
  5. 5.
    Sheng, S.: The Matching Uniqueness of T −shape Trees. Journal of Mathematical Study 32(1), 86–91 (1999)MathSciNetGoogle Scholar
  6. 6.
    Cvetkovic, D., Rowlinson, P.: The largest eigenvalue of a graph: A survey. Linear and Multilinear Algebra 28(1,2), 3–33 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Cvetkovic, D.M., Doob, M., Gutman, I., Torgaser, A.: Recent result in the theory of graph spectra. Elsevier Science Publishers, New York (1988)Google Scholar
  8. 8.
    Ma, H., Zhao, H.: The Matching Unique Graphs with Large Degree or Small Degree. Journal of Mathematical Research and Exposition 24(2), 369–373 (2004)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Ma, H., Ren, H.: The new methods for constructing matching-equivalence Graphs. Discrete Mathematics 307, 125–131 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Qiao, Y., Zhan, F.: Matching Uniqueness of T(1,4,n) and its Complement. Natural Science Journal of Hainan University 26(3), 220–224 (2008)MathSciNetGoogle Scholar
  11. 11.
    Zhan, F., Qiao, Y., Zhao, L.: The Matching Uniqueness of a Class of New Graphs. Journal of Southwest China Normal University (Natural Science Edition) 35(3), 7–11 (2010)Google Scholar
  12. 12.
    Shen, S.: On matching characterization of a Caterpillars. Pure and Applied Mathematics 26(4), 541–545 (2010)MathSciNetzbMATHGoogle Scholar
  13. 13.
    Shen, S.: On Matching Characterization of K 1 ∪ T(1,3,n) and Its Complement. Journal of Southwest China Normal University (Natural Science Edition) 34(3), 5–9 (2009)MathSciNetGoogle Scholar
  14. 14.
    Zhang, G., Li, Y.: A Lower Bound for the Second Largest Eigenvalue of a Class of Tree Matching. Journal of North University of China (Natural Science Edition) 32(1), 1–3 (2011)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Youfu Qiao
    • 1
  • Fuqin Zhan
    • 1
  1. 1.Department of MathematicsHechi UniversityYizhouChina

Personalised recommendations