On the Numbers of Cut-Vertices and End-Blocks in 4-Regular Graphs

Abstract

A cut-vertex in a graph G is a vertex whose removal increases the number of connected components of G. An end-block of G is a block with a single cut-vertex. In this paper we establish upper bounds on the numbers of end-blocks and cut-vertices in a 4-regular graph G and claw-free 4-regular graphs. We characterize the extremal graphs achieving these bounds.

Keywords

• 4-regular graph
• claw-free
• cut-vertices
• end-blocks