Circular Planar Electrical Networks, Split Systems, and Phylogenetic Networks

Autor:	Stefan Forcey
Rok vydání:	2023
Předmět:	Algebra and Number Theory Applied Mathematics FOS: Mathematics Mathematics - Combinatorics Combinatorics (math.CO) Geometry and Topology 05C50 05C10 92D15 94C15
Zdroj:	SIAM Journal on Applied Algebra and Geometry. 7:49-76
ISSN:	2470-6566
DOI:	10.1137/22m1473844
Popis:	We study a new invariant of circular planar electrical networks, well known to phylogeneticists: the circular split system. We use our invariant to answer some open questions about levels of complexity of networks and their related Kalmanson metrics. The key to our analysis is the realization that certain matrices arising from weighted split systems are studied in another guise: the Kron reductions of Laplacian matrices of planar electrical networks. Specifically we show that a response matrix of a circular planar electrical network corresponds to a unique resistance metric obeying the Kalmanson condition, and thus a unique weighted circular split system. Our results allow interchange of methods: phylogenetic reconstruction using theorems about electrical networks, and circuit reconstruction using phylogenetic techniques. 23 pages
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4fa63537051d26125aa424f06be9958f https://doi.org/10.1137/22m1473844 Zobrazit plný text záznamu