Discussiones Mathematicae Graph Theory 26(3) (2006) 403-412
doi: 10.7151/dmgt.1332

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ON ARBITRARILY VERTEX DECOMPOSABLE UNICYCLIC GRAPHS WITH DOMINATING CYCLE

Sylwia Cichacz  and  Irmina A. Zioło

Faculty of Applied Mathematics
AGH University of Science and Technology
Al. A. Mickiewicza 30, 30-059 Kraków, Poland
e-mail: cichacz@agh.edu.pl
e-mail: ziolo@agh.edu.pl

Abstract

A graph G of order n is called arbitrarily vertex decomposable if for each sequence (n1,☐,nk) of positive integers such that ∑ki = 1 ni = n, there exists a partition (V1,☐,Vk) of vertex set of G such that for every i ∈ {1,☐,k} the set Vi induces a connected subgraph of G on ni vertices. We consider arbitrarily vertex decomposable unicyclic graphs with dominating cycle. We also characterize all such graphs with at most four hanging vertices such that exactly two of them have a common neighbour.

Keywords: arbitrarily vertex decomposable graph, dominating cycle.

2000 Mathematics Subject Classification: 05C35, 05C38, 05C99.

References

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Received 30 November 2005
Revised 31 March 2006