Eigenspaces for \(-2\) in signed line graphs
It is known that \(-2\) appears in the spectrum of a connected signed line graph if and only if its root is either (a) a balanced signed graph, not a tree, that spans a switching of the complete signed graph or (b) an unbalanced simply signed graph, not a unicyclic simply signed graph, that spans...
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| Format: | Article |
| Language: | English |
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American Journal of Combinatorics
2025-05-01
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| Series: | The American Journal of Combinatorics |
| Subjects: | |
| Online Access: | https://ajcombinatorics.org/ojs/index.php/AmJC/article/view/31 |
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| Summary: | It is known that \(-2\) appears in the spectrum of a connected signed line graph if and only if its root is either (a) a balanced signed graph, not a tree, that spans a switching of the complete signed graph or (b) an unbalanced simply signed graph, not a unicyclic simply signed graph, that spans a switching of the signed doubled complete graph. In this paper, we compute the eigenspaces for $-2$ of these signed line graphs. The contribution can be seen as an alternative to [Discrete Appl. Math. 207 (2016) 29--38]. |
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| ISSN: | 2768-4202 |