Research Article

ON SIZE, ORDER, DIAMETER AND VERTEX-CONNECTIVITY

Volume: 1 Number: 1 January 2, 2019
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ON SIZE, ORDER, DIAMETER AND VERTEX-CONNECTIVITY

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.

Keywords

References

  1. F.R.K. Chung, The average distance and the independence number, J. Graph Theory. 12 (1988) 229-235.
  2. 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.
  3. P. Dankelmann, L. Volkmann, Minimum size of a graph or digraph of given radius, Inform. Process. Lett. 109(2009), 971{973.
  4. S. Mukwembi, On size, order, diameter and minimum degree, Indian J. Pure Appl. Math. 44 (2013) 467{472.
  5. 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.
  6. A. Tripathi, S. Vijay, On the least size of a graph with a given degree set, Discrete Appl. Math. 154 (2006) 2530{2536.
  7. V. Vizing, The number of edges in a graph of given radius, Soviet. Math. Dokl.8 (1967) 535-536.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Simon Mukwembi This is me

Publication Date

January 2, 2019

Submission Date

May 28, 2018

Acceptance Date

September 17, 2018

Published in Issue

Year 1970 Volume: 1 Number: 1

IZ

https://izlik.org/JA26KB62HF

Cite

RIS / Bibtex
APA
Munyira, S., & Mukwembi, S. (2019). ON SIZE, ORDER, DIAMETER AND VERTEX-CONNECTIVITY. MATI, 1(1), 21-24. https://izlik.org/JA26KB62HF
AMA
1.Munyira S, Mukwembi S. ON SIZE, ORDER, DIAMETER AND VERTEX-CONNECTIVITY. Mati. 2019;1(1):21-24. https://izlik.org/JA26KB62HF
Chicago
Munyira, Sheunesu, and Simon Mukwembi. 2019. “ON SIZE, ORDER, DIAMETER AND VERTEX-CONNECTIVITY”. MATI 1 (1): 21-24. https://izlik.org/JA26KB62HF.
EndNote
Munyira S, Mukwembi S (January 1, 2019) ON SIZE, ORDER, DIAMETER AND VERTEX-CONNECTIVITY. MATI 1 1 21–24.
IEEE
[1]S. Munyira and S. Mukwembi, “ON SIZE, ORDER, DIAMETER AND VERTEX-CONNECTIVITY”, Mati, vol. 1, no. 1, pp. 21–24, Jan. 2019, [Online]. Available: https://izlik.org/JA26KB62HF
ISNAD
Munyira, Sheunesu - Mukwembi, Simon. “ON SIZE, ORDER, DIAMETER AND VERTEX-CONNECTIVITY”. MATI 1/1 (January 1, 2019): 21-24. https://izlik.org/JA26KB62HF.
JAMA
1.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, Jan. 2019, pp. 21-24, https://izlik.org/JA26KB62HF.
Vancouver
1.Sheunesu Munyira, Simon Mukwembi. ON SIZE, ORDER, DIAMETER AND VERTEX-CONNECTIVITY. Mati [Internet]. 2019 Jan. 1;1(1):21-4. Available from: https://izlik.org/JA26KB62HF