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

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Wang D., Shan E.

Discussiones Mathematicae Graph Theory

2014

tom 34

nr 1

127-136

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.

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Lower bounds for the domination number

100%

Delaviña E., Pepper R., Waller B.

Discussiones Mathematicae Graph Theory

2010

tom 30

nr 3

475-487

In this note, we prove several lower bounds on the domination number of simple connected graphs. Among these are the following: the domination number is at least two-thirds of the radius of the graph, three times the domination number is at least two more than the number of cut-vertices in the graph, and the domination number of a tree is at least as large as the minimum order of a maximal matching.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

1 Delaviña E.

1 Pepper R.

1 Shan E.

1 Waller B.

1 Wang D.

1 2014

1 2010

Wyniki wyszukiwania

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

Lower bounds for the domination number