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Year 2019, Volume: 1 Issue: 1, 21 - 24, 02.01.2019

Abstract

References

  • F.R.K. Chung, The average distance and the independence number, J. Graph Theory. 12 (1988) 229-235.
  • P. Dankelmann, G.S. Domke, W. Goddard, P. Grobler J.H. Hattingh, H.C Swart, Maximum sizes of graphs with given domination parameters, DiscreteMath. 281 (2004) 137{148.
  • P. Dankelmann, L. Volkmann, Minimum size of a graph or digraph of given radius, Inform. Process. Lett. 109(2009), 971{973.
  • S. Mukwembi, On size, order, diameter and minimum degree, Indian J. Pure Appl. Math. 44 (2013) 467{472.
  • O. Ore, Diameters in graphs, J. Combin. Theory 5 (1968) 75{81.Z. Tao, X. Junming, L. Jun, On diameters and average distance of graphs, Transactions 8 (2004) 1{6.
  • A. Tripathi, S. Vijay, On the least size of a graph with a given degree set, Discrete Appl. Math. 154 (2006) 2530{2536.
  • V. Vizing, The number of edges in a graph of given radius, Soviet. Math. Dokl.8 (1967) 535-536.

ON SIZE, ORDER, DIAMETER AND VERTEX-CONNECTIVITY

Year 2019, Volume: 1 Issue: 1, 21 - 24, 02.01.2019

Abstract

Let G be a nite connected graph. We give an asymptotically sharp upper bound on the size of G in terms of its order, diameter and vertex-connectivity. The result is a strengthening of an old classical theorem of Ore [5] if vertex-connectivity is prescribed and constant.

References

  • F.R.K. Chung, The average distance and the independence number, J. Graph Theory. 12 (1988) 229-235.
  • P. Dankelmann, G.S. Domke, W. Goddard, P. Grobler J.H. Hattingh, H.C Swart, Maximum sizes of graphs with given domination parameters, DiscreteMath. 281 (2004) 137{148.
  • P. Dankelmann, L. Volkmann, Minimum size of a graph or digraph of given radius, Inform. Process. Lett. 109(2009), 971{973.
  • S. Mukwembi, On size, order, diameter and minimum degree, Indian J. Pure Appl. Math. 44 (2013) 467{472.
  • O. Ore, Diameters in graphs, J. Combin. Theory 5 (1968) 75{81.Z. Tao, X. Junming, L. Jun, On diameters and average distance of graphs, Transactions 8 (2004) 1{6.
  • A. Tripathi, S. Vijay, On the least size of a graph with a given degree set, Discrete Appl. Math. 154 (2006) 2530{2536.
  • V. Vizing, The number of edges in a graph of given radius, Soviet. Math. Dokl.8 (1967) 535-536.
There are 7 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Sheunesu Munyira

Simon Mukwembi This is me

Publication Date January 2, 2019
Acceptance Date September 17, 2018
Published in Issue Year 2019 Volume: 1 Issue: 1

Cite

APA Munyira, S., & Mukwembi, S. (2019). ON SIZE, ORDER, DIAMETER AND VERTEX-CONNECTIVITY. MATI, 1(1), 21-24.
AMA Munyira S, Mukwembi S. ON SIZE, ORDER, DIAMETER AND VERTEX-CONNECTIVITY. Mati. January 2019;1(1):21-24.
Chicago Munyira, Sheunesu, and Simon Mukwembi. “ON SIZE, ORDER, DIAMETER AND VERTEX-CONNECTIVITY”. MATI 1, no. 1 (January 2019): 21-24.
EndNote Munyira S, Mukwembi S (January 1, 2019) ON SIZE, ORDER, DIAMETER AND VERTEX-CONNECTIVITY. MATI 1 1 21–24.
IEEE S. Munyira and S. Mukwembi, “ON SIZE, ORDER, DIAMETER AND VERTEX-CONNECTIVITY”, Mati, vol. 1, no. 1, pp. 21–24, 2019.
ISNAD Munyira, Sheunesu - Mukwembi, Simon. “ON SIZE, ORDER, DIAMETER AND VERTEX-CONNECTIVITY”. MATI 1/1 (January 2019), 21-24.
JAMA Munyira S, Mukwembi S. ON SIZE, ORDER, DIAMETER AND VERTEX-CONNECTIVITY. Mati. 2019;1:21–24.
MLA Munyira, Sheunesu and Simon Mukwembi. “ON SIZE, ORDER, DIAMETER AND VERTEX-CONNECTIVITY”. MATI, vol. 1, no. 1, 2019, pp. 21-24.
Vancouver Munyira S, Mukwembi S. ON SIZE, ORDER, DIAMETER AND VERTEX-CONNECTIVITY. Mati. 2019;1(1):21-4.