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## On size, order, diameter and vertex-connectivity

#### Sheunesu MUNYİRA [1] , Simon MUKWEMBİ [2]

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.
size, vertex-connectivity, diameter
• 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.
Primary Language en Mathematics Articles Author: Sheunesu MUNYİRA (Primary Author)Country: Turkey Author: Simon MUKWEMBİ Publication Date : January 2, 2019
 Bibtex @research article { mati427877, journal = {MATI}, issn = {2636-7785}, address = {}, publisher = {Süleyman EDİZ}, year = {2019}, volume = {1}, pages = {21 - 24}, doi = {}, title = {On size, order, diameter and vertex-connectivity}, key = {cite}, author = {Munyi̇ra, Sheunesu and Mukwembi̇, Simon} } APA Munyi̇ra, S , Mukwembi̇, S . (2019). On size, order, diameter and vertex-connectivity . MATI , 1 (1) , 21-24 . Retrieved from https://dergipark.org.tr/en/pub/mati/issue/38227/427877 MLA Munyi̇ra, S , Mukwembi̇, S . "On size, order, diameter and vertex-connectivity" . MATI 1 (2019 ): 21-24 Chicago Munyi̇ra, S , Mukwembi̇, S . "On size, order, diameter and vertex-connectivity". MATI 1 (2019 ): 21-24 RIS TY - JOUR T1 - On size, order, diameter and vertex-connectivity AU - Sheunesu Munyi̇ra , Simon Mukwembi̇ Y1 - 2019 PY - 2019 N1 - DO - T2 - MATI JF - Journal JO - JOR SP - 21 EP - 24 VL - 1 IS - 1 SN - 2636-7785- M3 - UR - Y2 - 2018 ER - EndNote %0 MATI On size, order, diameter and vertex-connectivity %A Sheunesu Munyi̇ra , Simon Mukwembi̇ %T On size, order, diameter and vertex-connectivity %D 2019 %J MATI %P 2636-7785- %V 1 %N 1 %R %U ISNAD Munyi̇ra, Sheunesu , Mukwembi̇, Simon . "On size, order, diameter and vertex-connectivity". MATI 1 / 1 (January 2019): 21-24 . AMA Munyi̇ra S , Mukwembi̇ S . On size, order, diameter and vertex-connectivity. Mati. 2019; 1(1): 21-24. Vancouver Munyi̇ra S , Mukwembi̇ S . On size, order, diameter and vertex-connectivity. MATI. 2019; 1(1): 21-24.

Authors of the Article
[2]