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

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

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. W...

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Bibliographic Details
Main Authors: Wang Dingguo, Shan Erfang
Format: Article
Language:English
Published: University of Zielona Góra 2014-02-01
Series:Discussiones Mathematicae Graph Theory
Subjects:
4-regular graph
claw-free
cut-vertices
end-blocks
Online Access:https://doi.org/10.7151/dmgt.1724
Description
Summary: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.
ISSN:2083-5892

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