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.
Articolo in rivista - Articolo scientifico
p-majorization; p-Schur-convex functions; graphs; weighted global; cyclicity index
English
11
Gold Open Access
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].
Bianchi, M; Cornaro, A; Palacios, J; Torriero, A
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/334772
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