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Proyecciones (Antofagasta)

versión impresa ISSN 0716-0917

Proyecciones (Antofagasta) vol.30 no.1 Antofagasta  2011

http://dx.doi.org/10.4067/S0716-09172011000100001 

Proyecciones Journal of Mathematics
Vol. 30, N° 1, pp. 1-17, May 2011.
Universidad Católica del Norte
Antofagasta - Chile


Cycle connectivity in weighted graphs


Sunil Mathew
M. S. Sunitha

National institute of technology, India


Correspondencia a:


Abstract

Some new connectivity concepts in weighted graphs are introduced in this article. The concepts of strong arc, partial cutnode, bridge and block are introduced. Also three different types of cycles namely locamin cycle, multimin cycle and strongest strong cycle are introduced. Partial blocks in weighted graphs are characterized using strongest paths. Also a set of necessary conditions for a weighted graph to be a partial block involving strong cycles and a sufficient condition for a weighted graph to be a partial block involving strongest strong cycles are obtained. A new connectivity parameter called cycle connectivity and a new type of weighted graphs called θ - weighted graphs are introduced and partial blocks in θ - weighted graphs are fully characterized.

AMS classification :05C22, 05C38, 05C40.

Keywords : Weighted graph, partial cutnode, partial bridge, strong cycle, cycle connectivity.


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References

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Sunil Mathew
Department of Mathematics
National Institute of Technology
Calicut - 673 601
India
e-mail : sm@nitc.ac.in


M. S. Sunitha
Department of Mathematics
National Institute of Technology
Calicut - 673 601
India
e-mail : sunitha@nitc.ac.in


Received : August 2010. Accepted : December 2010