Signed (0,2)-graphs with few eigenvalues and a symmetric spectrum
We investigate properties of signed graphs that have few distinct eigenvalues together with a symmetric spectrum. Our main contribution is to determine all signed rectagraphs (triangle-free signed (Formula presented.) -graphs) with vertex degree at most 6 that have precisely two distinct eigenvalues...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
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2022
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| Online Access: | https://hdl.handle.net/10356/162136 |
| _version_ | 1811678320732930048 |
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| author | Greaves, Gary Royden Watson Stanić, Zoran |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Greaves, Gary Royden Watson Stanić, Zoran |
| author_sort | Greaves, Gary Royden Watson |
| collection | NTU |
| description | We investigate properties of signed graphs that have few distinct eigenvalues together with a symmetric spectrum. Our main contribution is to determine all signed rectagraphs (triangle-free signed (Formula presented.) -graphs) with vertex degree at most 6 that have precisely two distinct eigenvalues (Formula presented.). Next, we consider to what extent induced subgraphs of signed graph with two distinct eigenvalues (Formula presented.) are determined by their spectra. Lastly, we classify signed rectagraphs that have a symmetric spectrum with three distinct eigenvalues and give a partial classification for signed (Formula presented.) -graphs with four distinct eigenvalues. |
| first_indexed | 2024-10-01T02:51:24Z |
| format | Journal Article |
| id | ntu-10356/162136 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T02:51:24Z |
| publishDate | 2022 |
| record_format | dspace |
| spelling | ntu-10356/1621362022-10-05T02:28:10Z Signed (0,2)-graphs with few eigenvalues and a symmetric spectrum Greaves, Gary Royden Watson Stanić, Zoran School of Physical and Mathematical Sciences Science::Mathematics Adjacency Matrix Bipartite Double We investigate properties of signed graphs that have few distinct eigenvalues together with a symmetric spectrum. Our main contribution is to determine all signed rectagraphs (triangle-free signed (Formula presented.) -graphs) with vertex degree at most 6 that have precisely two distinct eigenvalues (Formula presented.). Next, we consider to what extent induced subgraphs of signed graph with two distinct eigenvalues (Formula presented.) are determined by their spectra. Lastly, we classify signed rectagraphs that have a symmetric spectrum with three distinct eigenvalues and give a partial classification for signed (Formula presented.) -graphs with four distinct eigenvalues. Ministry of Education (MOE) The first author was supported in part by the Singapore Ministry of Education Academic Research Fund (Tier 1); grant number RG21/20. The second author was supported by the Science Fund of the Republic of Serbia; grant number 7749676: Spectrally Constrained Signed Graphs with Applications in Coding Theory and Control Theory—SCSG‐ctct. 2022-10-05T02:28:10Z 2022-10-05T02:28:10Z 2022 Journal Article Greaves, G. R. W. & Stanić, Z. (2022). Signed (0,2)-graphs with few eigenvalues and a symmetric spectrum. Journal of Combinatorial Designs, 30(5), 332-353. https://dx.doi.org/10.1002/jcd.21828 1063-8539 https://hdl.handle.net/10356/162136 10.1002/jcd.21828 2-s2.0-85124471280 5 30 332 353 en RG21/20 Journal of Combinatorial Designs © 2022 Wiley Periodicals LLC. All rights reserved. |
| spellingShingle | Science::Mathematics Adjacency Matrix Bipartite Double Greaves, Gary Royden Watson Stanić, Zoran Signed (0,2)-graphs with few eigenvalues and a symmetric spectrum |
| title | Signed (0,2)-graphs with few eigenvalues and a symmetric spectrum |
| title_full | Signed (0,2)-graphs with few eigenvalues and a symmetric spectrum |
| title_fullStr | Signed (0,2)-graphs with few eigenvalues and a symmetric spectrum |
| title_full_unstemmed | Signed (0,2)-graphs with few eigenvalues and a symmetric spectrum |
| title_short | Signed (0,2)-graphs with few eigenvalues and a symmetric spectrum |
| title_sort | signed 0 2 graphs with few eigenvalues and a symmetric spectrum |
| topic | Science::Mathematics Adjacency Matrix Bipartite Double |
| url | https://hdl.handle.net/10356/162136 |
| work_keys_str_mv | AT greavesgaryroydenwatson signed02graphswithfeweigenvaluesandasymmetricspectrum AT staniczoran signed02graphswithfeweigenvaluesandasymmetricspectrum |