Skip to main content

Some path-length properties of graphs and digraphs

Contributed Papers

  • 1057 Accesses

Part of the Lecture Notes in Mathematics book series (LNM,volume 885)

Keywords

  • Adjacency Matrix
  • Regular Graph
  • Incidence Matrix
  • Association Scheme
  • Combinatorial Theory

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   69.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. W. Ahrens and G. Szekeres, On a combinatorial generalization of the 27 lines associated with a cubic surface, J. Austral. Math. Soc., 10 (1969), 485–492.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. W. G. Bridges, The polynomial of a non-regular digraph, Pacific J. Math., 38 (1971), 325–342.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. W. G. Bridges, The regularity of X3-graphs, J. Combinatorial Theory, 12 (1972), 174–176.

    CrossRef  MathSciNet  MATH  Google Scholar 

  4. W. G. Bridges, A class of normal (0.1)-matrices, Can. J. Math., 25 (1973), 621–626.

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. W. G. Bridges, D. M. Finucane and R. A. Mena, On graphs with unique 2-paths for unjoined vertices, J. C. I. S. S., 2 (1977), 12–19.

    MathSciNet  MATH  Google Scholar 

  6. W. G. Bridges and R. A. Mena, Multiplicative designs I: the reducible cases, J. Combinatorial Theory (A), 27 (1979), 69–84.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. W. G. Bridges and R. A. Mena, Multiplicative designs II: uniform normals and related structures, to appear in J. Combinatorial Theory (A).

    Google Scholar 

  8. W. G. Bridges and R. A. Mena, Xk-digraphs, to appear in J. Combinatorial Theory (B).

    Google Scholar 

  9. W. G. Bridges and Sam Toueg, On the Impossibility of directed Moore graphs, to appear in J. Combinatorial Theory (B).

    Google Scholar 

  10. W. G. Bridges and R. A. Mena, Multiplicative cones—a family of three eigenvalue graphs, (submitted).

    Google Scholar 

  11. W. G. Bridges and R. A. Mena, Rational circulants with rational spectra and cyclic strongly regular graphs, to appear in Ars Combinatoria.

    Google Scholar 

  12. B. Elspas and J. Turner, Graphs with circulant adjacency matrices, J. Combinatorial Theory, 9 (1970), 297–307.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. W. M. Kanter, Moore geometries and rank 3 groups having μ=1, Quarterly J. Math. Oxford, 28 (1977), 309–328.

    CrossRef  MathSciNet  Google Scholar 

  14. J. B. Kelly, A characteristic property of quadratic residues, Proc. Amer. Math. Soc., 5 (1954), 38–46.

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. Clement W. H. Lam, A generalization of cyclic difference sets I, J. Combinatorial Theory (A), 19 (1975), 51–65.

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. Clement W. H. Lam, A generalization of cyclic difference sets II, J. Combinatorial Theory (A), 19 (1075), 177–191.

    CrossRef  MATH  Google Scholar 

  17. Clement W. H. Lam, On some solutions of Ak=dI+λJ, J. Combinatorial Theory (A), 23 (1977), 140–147.

    CrossRef  Google Scholar 

  18. Clement W. H. Lam, Rational 9-circulants satisfying the matrix equation A2=dI+γJ, Thesis, Calif, Inst. of Tech., 1974.

    Google Scholar 

  19. Clement W. H. Lam and J. H. VanLint, Directed graphs with unique paths of fixed length, J. Combinatorial Theory (B), 24 (1978), 331–337.

    CrossRef  MathSciNet  Google Scholar 

  20. Ho-Jin Lee, A note on geodetic graphs of diameter two and their relation to orthogonal latin squares, J. Combinatorial Theory (B), 22 (1977), 165–167.

    CrossRef  MathSciNet  MATH  Google Scholar 

  21. H. J. Ryser, A generalization of the matrix equation A2=J, Linear Algebra and Appl., 3 (1970), 451–460.

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. J. J. Seidel, Strongly regular graphs with (−1, 1,0) adjacency matrix having eigenvalue 3, Linear Algebra and Appl., 1 (1968), 281–298.

    CrossRef  MathSciNet  MATH  Google Scholar 

  23. J. G. Stemple, Geodetic graphs of diameter two, J. Combinatorial Theory, 17 (1974), 266–280.

    CrossRef  MathSciNet  MATH  Google Scholar 

  24. J. G. Stemple and M. E. Watkins, On planar geodetic graphs, J. Combinatorial Theory, 4 (1968), 101–117.

    CrossRef  MathSciNet  MATH  Google Scholar 

  25. M. Tuero, A contribution to the theory of cyclic graphs, Matrix and Tensor Quarterly (1961), 74–80.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1981 Springer-Verlag

About this paper

Cite this paper

Bridges, W.G. (1981). Some path-length properties of graphs and digraphs. In: Rao, S.B. (eds) Combinatorics and Graph Theory. Lecture Notes in Mathematics, vol 885. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0092262

Download citation

  • DOI: https://doi.org/10.1007/BFb0092262

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11151-1

  • Online ISBN: 978-3-540-47037-3

  • eBook Packages: Springer Book Archive