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Abstract
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International Journal of Mathematics and Mathematical Sciences
Volume 12 (1989), Issue 2, Pages 305-308
doi:10.1155/S0161171289000359

On the number of cut-vertices in a graph

Glenn Hopkins and William Staton

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

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.