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Mathematics > Spectral Theory

Title: The spectral geometry of biregular graphs: a quantum graph approach

Authors: Robert Carlson
(Submitted on 17 May 2023 (v1), last revised 19 May 2023 (this version, v2))
Abstract: The spectral theory of the Laplace differential operator for biregular quantum graphs is developed. Trees are studied in detail. Generating functions for closed non backtracking walks appear when resolvents for trees are related to resolvents for biregular graphs they cover. The relationship between resolvent traces for finite graphs and walk generating functions is especially productive. A detailed description of the rational extension of nonbacktracking walk generating functions is presented.
Comments: Errors in the last subsection of the first version were corrected
Subjects: Spectral Theory (math.SP)
MSC classes: 34B45 (primary) O5C50 (secondary)
Cite as: arXiv:2305.10537 [math.SP]
  (or arXiv:2305.10537v2 [math.SP] for this version)

Submission history

From: Robert Carlson [view email]
[v1] Wed, 17 May 2023 19:49:08 GMT (21kb)
[v2] Fri, 19 May 2023 20:03:33 GMT (21kb)
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