In this paper we define a new graph-theoretic cyclicity index CW(G) as a natural generalization of the global cyclicity index C(G) when arbitrary resistances are allocated to each edge of an electrical network. Upper and lower bounds for CW(G) are then provided using a powerful technique, based on p-majorization, which extends our prior studies (Bianchi et al. in Discrete Appl. Math., 2014, doi: 10.1016/j.dam.2014.10.037; Bianchi et al. in Math. Inequal. Appl. 16(2): 329-347, 2013). These new results on weighted majorization are of interest in themselves and may be applied also in other scenarios.
Bianchi, M., Cornaro, A., Palacios, J., Torriero, A. (2015). Bounds for the global cyclicity index of a general network via weighted majorization. JOURNAL OF INEQUALITIES AND APPLICATIONS, 2015(1) [10.1186/s13660-015-0624-5].
Bounds for the global cyclicity index of a general network via weighted majorization
Cornaro A
;
2015
Abstract
In this paper we define a new graph-theoretic cyclicity index CW(G) as a natural generalization of the global cyclicity index C(G) when arbitrary resistances are allocated to each edge of an electrical network. Upper and lower bounds for CW(G) are then provided using a powerful technique, based on p-majorization, which extends our prior studies (Bianchi et al. in Discrete Appl. Math., 2014, doi: 10.1016/j.dam.2014.10.037; Bianchi et al. in Math. Inequal. Appl. 16(2): 329-347, 2013). These new results on weighted majorization are of interest in themselves and may be applied also in other scenarios.
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