Cycle connectivity in weighted graphs

Authors

  • Sunil Mathew National Institute of Technology.
  • M. S. Sunitha National Institute of Technology.

DOI:

https://doi.org/10.4067/S0716-09172011000100001

Keywords:

Weighted graph, Partial cutnode, Partial bridge, Strong cycle, Cycle connectivity.

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.

Author Biographies

Sunil Mathew, National Institute of Technology.

Department of Mathematics.

M. S. Sunitha, National Institute of Technology.

Department of Mathematics.

References

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[6] Sunil Mathew, M. S. Sunitha, Types of arcs in a fuzzy graph, Information Sciences 179 (11)1, pp. 1760-1768, (2009).

[7] Sunil Mathew, M. S. Sunitha, Some connectivity concepts in weighted graphs, Advances and Applications in Discrete Mathematics 6 (1), pp. 45-54, (2010).

[8] Sunil Mathew, M. S. Sunitha, Bonds in graphs and fuzzy graphs,Advances in Fuzzy Sets and Systems, 6 (2), pp. 107-119, (2010).

[9] S. Zang, X. Li, H. Broersma, Heavy paths and cycles in weighted graphs, Discrete Math. 223, pp. 327-336, (2000).

Published

2011-05-25

How to Cite

[1]
S. Mathew and M. S. Sunitha, “Cycle connectivity in weighted graphs”, Proyecciones (Antofagasta, On line), vol. 30, no. 1, pp. 1-17, May 2011.

Issue

Section

Artículos