Graphs determined by their \(T\)-gain spectra

Authors

  • S. Wang
  • D. Wong
  • F. Tian

Keywords:

Complex unit gain graphs, graphs determined by their spectra, cospectral graphs

Abstract

An undirected graph G is said to be determined by its T-gain spectrum (DTS) if every T-gain graph Φ = (H, T, φ) cospectral to G is switching equivalent to G. In this paper, we obtain the following results (1) The complete graph Kn and the graph Kn, obtained from Kn by deleting an edge, are proved to be DTS. (2) The star K1,n is DTS if and only if n ≤ 2. (3) An odd path P2m+1 is not DTS if m ≥ 2. (4) An operation is given for constructing cospectral T-gain graphs. As an application, a tree of arbitrary order (at least 5) is proved to be not DTS.

Published

2021-03-10

Issue

Vol. 103 No. 2 (2021)

Section

Articles
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