Loading...
Loading...

Go to the content (press return)

The Kirchhoff index of unicycle weighted chains

Author
Carmona, A.; Encinas, A.; Mitjana, M.
Type of activity
Journal article
Journal
Electronic notes in discrete mathematics
Date of publication
2014-09-16
Volume
46
First page
217
Last page
224
DOI
https://doi.org/10.1016/j.endm.2014.08.029 Open in new window
Project funding
Control de invariantes en grafos sujetos a propiedades estructurales
Optimización y problemas extremales en teoria de grafos y combinatoria. Aplicacions a les redes de comunicación
URL
http://www.sciencedirect.com/science/article/pii/S1571065314000304 Open in new window
Abstract
We consider a class of generalized linear chains, namely, the unicycle chains as a perturbation of a 2n–path by adding one weighted edge between two specific vertices. This class of chains includes, in particular, the weighted cycle. In this work, we obtain the Green function, the effective resistance and the Kirchhoff index of the unicycle chains as a function of the Green function, the effective resistance and the Kirchhoff index of a path, respectively.
Keywords
Unicycle network
Group of research
MAPTHE - Matrix Analysis and Discrete Potential Theory