Name
Title | ||
|---|---|---|
???????A new criterion for almost controllable graphs being determined by their generalized spectra |
Abstract | ||
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Let G be a graph on n vertices with adjacency matrix A(G) and let e be the all-one vector. Then the walk-matrix of G is defined as W(G)=[e,A(G)e, A(2)(G)e, horizontexpressionl ellipsis ,A(n-1)(G)e]. We call G controllable if W(G) is non-singular and almost controllable if the rank of W(G) is n-1. In Wang (2017) [11], the author gave a simple arithmetic criterion for a family of controllable graphs to be determined by their generalized spectra. However, the method fails for non-controllable graphs. In this paper, we give a new simple criterion for an almost controllable graph to be determined by its generalized spectrum, which improves upon the existing results. (C) 2022 Elsevier B.V. All rights reserved. |
Year | DOI | Venue |
|---|---|---|
2022 | 10.1016/j.disc.2022.113060 | DISCRETE MATHEMATICS |
Keywords | DocType | Volume |
Almost controllable graph, Generalized spectrum, Determined by spectrum, Rational orthogonal matrix | Journal | 345 |
Issue | ISSN | Citations |
11 | 0012-365X | 0 |
PageRank | References | Authors |
0.34 | 0 | 3 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Lihong Qiu | 1 | 0 | 0.68 |
| Wei Wang | 2 | 81 | 12.64 |
| Hao Zhang | 3 | 9 | 17.86 |