How the permutation of edges of a metric graph affects the number of points moving along the edges

2014/10/18 by В. Л. Чернышев, V. L. Chernyshev, Chernyshev, V. L. +3
Computer Science · Mathematics · Physics and Astronomy · #Advanced Graph Theory Research #Coding theory and cryptography #FOS: Physical sciences #Graph Labeling and Dimension Problems #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.1410.5015

arxiv created 2014/10/18 · openalex publication_date 2014/10/18 · arxiv updated 2014/10/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We consider a dynamical system on a metric graph, that corresponds to a semiclassical solution of a time-dependent Schrödinger equation. We omit all details concerning mathematical physics and work with a purely discrete problem. We find a weak inequality representation for the number of points coming out of the vertex of an arbitrary tree graph. We apply this construction to an "H-junction" graph. We calculate the difference between numbers of moving points corresponding to the permutation of edges. Then we find a symmetrical difference of the number of points moving along the edges of a metric graph.

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