Role of the Boundary Conditions in the Graphs Split at Vertices

Ławniczak, Michał; Farooq, Omer; Akhshani, A.; Białous, Małgorzata; Bauch, Szymon; Sirko, Leszek

doi:10.1007/978-3-031-27082-6_14

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A Graph Split At Edges and Vertices Into Two Subgraphs1

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2023

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“…In this article we consider a general situation when an original graph . Simpler situations of quantum graphs split only at vertices or at edges were considered in [66,67] and [68], respectively.…”

Section: A Graph Split At Edges and Vertices Into Two Subgraphsmentioning

confidence: 99%

Investigation of the generalized Euler characteristic of graphs and microwave networks split at edges and vertices

et al. 2023

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We analyze the situation when the original graph is split at edges and vertices into two disconnected subgraphs. We show that there is a relationship between the generalized Euler characteristic Eo(|VDo|) of the original graph and the generalized Euler characteristics Ei(|VDi|), i = 1, 2, of two disconnected subgraphs, where |VDo| and |VDi|, i = 1, 2, are the numbers of vertices with the Dirichlet boundary conditions in the graphs. Theoretical predictions are veriﬁed experimentally using microwave networks which simulate quantum graphs.

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Section: A Graph Split At Edges and Vertices Into Two Subgraphsmentioning

confidence: 99%