Skip to main content
SpringerLink
Log in

On double bound graphs with respect to graph operations

  • Conference paper
  • First Online:
Book cover Discrete and Computational Geometry (JCDCG 2000)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2098))

Included in the following conference series:

  • 567 Accesses

Abstract

We consider upper bound graphs with respect to operations on graphs, for example, the sum, the Cartesian product, the corona and the middle graphs of graphs, etc. According to the characterization of double bound graphs, we deal with characterizations of double bound graphs obtained by graph operations. For example, The Cartesian product G × H of two graphs G and H is a DB-graph if and only if both G and H are bipartite graphs, the corona G º H of two graphs G and H is a DB-graph if and only if G is a bipartite graph and H is a UB-graph, and the middle graph M(G) of a graph G is a DB-graph if and only if G is an even cycle or a path, etc.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. M. Behzad and G. Chartrand, Total graphs and traversability, Proc. Edinburgh Math. Soc., 15 (1966)117–120.

    Article  MATH  MathSciNet  Google Scholar 

  2. D. Diny, The double bound graph of a partially ordered set, Journal of Combinatorics, Infomation & System Sciences, 10(1985),52–56.

    MATH  MathSciNet  Google Scholar 

  3. H. Era, K. Ogawa, and M. Tsuchiya, On upper bound graphs with respect to unary operations on graphs, (preprint).

    Google Scholar 

  4. H. Era, K. Ogawa, and M. Tsuchiya, On upper bound graphs with respect to operations on graphs, Theoretical Computer Science, 235(2)(2000),219–223.

    Article  MATH  MathSciNet  Google Scholar 

  5. H. Era and M. Tsuchiya, On upper bound graphs whose complements are also upper bound graphs, Discrete Mathematics, 197(1998),103–109.

    Article  MathSciNet  Google Scholar 

  6. T. Hamada and I. Yoshimura, Traversability and connectivity of the middle graph of a graph, Discrete Mathematics, 14(1976)247–255.

    Article  MATH  MathSciNet  Google Scholar 

  7. F. Harary, Graph Theory, (Addison-Wesley, 1969).

    Google Scholar 

  8. S.-I. Iwai, K. Ogawa and M. Tsuchiya, A note on construction of double bound graphs, (preprint).

    Google Scholar 

  9. F.R. McMorris and T. Zaslavsky, Bound graphs of a partially ordered set, Journal of Combinatorics, Infomation & System Sciences, 7(1982),134–138.

    MATH  MathSciNet  Google Scholar 

  10. K. Ogawa and M. Tsuchiya, On upper bound graphs with respect to line graphs, Southeast Asian Bulletin of Mathematics, 23(1999),265–269.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Tokai University, Hiratsuka, 259-1292, Japan

    Shin-ich Iwai

  2. Department of Mathematical Sciences, Tokai University, Hiratsuka, 259-1292, Japan

    Kenjiro Ogawa

  3. Department of Mathematical Sciences, Tokai University, Hiratsuka, 259-1292, Japan

    Morimasa Tsuchiya

Authors
  1. Shin-ich Iwai
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kenjiro Ogawa
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Morimasa Tsuchiya
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Research Institute of Educational Development, Tokai University, 2-28-4 Tomigaya, Shibuya-ku, Tokyo, 151-0063, Japan

    Jin Akiyama

  2. Department of Computer and Information Sciences, Ibaraki University, Hitachi, 316-8511, Japan

    Mikio Kano

  3. Department of Mathematics, Tokai University, 3-20-1 Orido Shimizu-shi, Shizuoka, 424-8610, Japan

    Masatsugu Urabe

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Iwai, Si., Ogawa, K., Tsuchiya, M. (2001). On double bound graphs with respect to graph operations. In: Akiyama, J., Kano, M., Urabe, M. (eds) Discrete and Computational Geometry. JCDCG 2000. Lecture Notes in Computer Science, vol 2098. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47738-1_15

Download citation

  • DOI: https://doi.org/10.1007/3-540-47738-1_15

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42306-5

  • Online ISBN: 978-3-540-47738-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation