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AKCE International Journal of Graphs and Combinatorics Volume 7, 2010 - Issue 1
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Articles

Structural properties of graphs of diameter 2 and defect 2

Minh Hoang NguyenSchool of Electrical Engineering and Computer Science Faculty of Engineering and Built Environment The University of Newcastle NSW 2308, Australia;Ericsson Australia Pty Ltd Tower B 112-118 Talavera Road NSW2113, Australia
,
Mirka MillerSchool of Electrical Engineering and Computer Science Faculty of Engineering and Built Environment The University of Newcastle NSW 2308, Australia;Department of Mathematics University of West Bohemia, Pilsen, Czech Republic;Department of Computer Science King's CollegeLondon, UK e-mail: [email protected], [email protected]
&
S. Arumugam
(Communicated by)
Pages 29-43 | Received 08 May 2008, Accepted 08 Sep 2009, Published online: 10 Mar 2020

References

  • Y.M. Cholily, E.T. Baskoro and S. Uttunggadewa, Some conditions for the existence of (d, k)-digraphs containing selfrepeat, Lecture Notes in Computer Science, 3330 (2005), 87–93.
  • P. Erdös, S. Fajtlowicz, A.J. Hoffman, Maximum degree in graphs of diameter 2, Networks, 10 (1980), 87–90.
  • A.J. Hoffman and R.R. Singleton, On Moore Graphs with diameters 2 and 3, IBM J. Res. Dev., 64M. (1960), 15–21.
  • J. Gimbert, On the existence of (d, k)-digraphs, Discrete Math., 197-198 (1999), 375–391.
  • J. Gimbert, Enumeration of almost Moore digraphs of diameter two, Discrete Math., 231M (2001), 177–190.
  • M. Miller, M.H. Nguyen and R. Simanjuntak, Repeat structures in regular graphs and digraphs, Proceedings of AWOCA'05, Ballarat, Australia, September 2005, pp.471–479.
  • M. Miller and J. Širáň, Moore graphs and beyond: A survey of the degree/diameter problem, Electronic Journal of Combinatorics, DS14 (2005), 1–61.
  • M.H. Nguyen and M. Miller, Structural properties of graphs of diameter 2 with maximal repeats, Discrete Math., 308 (2008), 2337–2341.

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