In this note, we use a procedure, proposed in [1], based on a majorization technique, which localizes real eigenvalues of a matrix of order n. Through this information, we compute a lower bound for the Kirchhoff index (see [3]) that takes advantage of additional eigenvalues bounds. An algorithm has been developed with MATLAB software to evaluate the above mentioned bound. Finally, numerical examples are provided showing how tighter results can be obtained.
Cornaro, A., Clemente, G. P., A New Lower Bound for the Kirchhoff Indexusing a numerical procedure based onMajorization Techniques, <<ELECTRONIC NOTES IN DISCRETE MATHEMATICS>>, 2013; 2013 (33): 383-390. [doi:10.1016/j.endm.2013.05.116] [http://hdl.handle.net/10807/43115]
A New Lower Bound for the Kirchhoff Index using a numerical procedure based on Majorization Techniques
Cornaro, Alessandra;Clemente, Gian Paolo
2013
Abstract
In this note, we use a procedure, proposed in [1], based on a majorization technique, which localizes real eigenvalues of a matrix of order n. Through this information, we compute a lower bound for the Kirchhoff index (see [3]) that takes advantage of additional eigenvalues bounds. An algorithm has been developed with MATLAB software to evaluate the above mentioned bound. Finally, numerical examples are provided showing how tighter results can be obtained.
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