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International Journal of Mathematics and Mathematical Sciences
Volume 12, Issue 2, Pages 305-308
http://dx.doi.org/10.1155/S0161171289000359

On the number of cut-vertices in a graph

Department of Mathematics, University of Mississippi, University 38677, MS, USA

Received 18 May 1987; Revised 8 September 1987

Copyright © 1989 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A connected graph with n vertices contains no more than r2r-2(n-2) cutvertices of degree r. All graphs in which the bound is achieved are described. In addition, for graphs of maximum degree three and minimum δ, best possible bounds are obtained for δ=1, 2, 3.