A note on graphs with purely imaginary per-spectrum
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866909182210342912 |
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| author | Singh, Ranveer Wankhede, Hitesh |
| author_facet | Singh, Ranveer Wankhede, Hitesh |
| contents | In 1983, Borowiecki and Jóźwiak posed the problem ``Characterize those graphs which have purely imaginary per-spectrum.'' This problem is still open. The most general result, although a partial solution, was given in 2004 by Yan and Zhang, who show that if $G$ is a bipartite graph containing no subgraph which is an even subdivision of $K_{2,3}$, then it has purely imaginary per-spectrum. Zhang and Li in 2012 proved that such graphs are planar and admit a Pfaffian orientation. In this article, we describe how to construct graphs with purely imaginary per-spectrum having a subgraph which is an even subdivision of $K_{2,3}$ (planar and nonplanar) using coalescence of rooted graphs. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2211_13072 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A note on graphs with purely imaginary per-spectrum Singh, Ranveer Wankhede, Hitesh Combinatorics Discrete Mathematics 05C05, 05C31, 05C50, 05C76 G.2.1; G.2.2 In 1983, Borowiecki and Jóźwiak posed the problem ``Characterize those graphs which have purely imaginary per-spectrum.'' This problem is still open. The most general result, although a partial solution, was given in 2004 by Yan and Zhang, who show that if $G$ is a bipartite graph containing no subgraph which is an even subdivision of $K_{2,3}$, then it has purely imaginary per-spectrum. Zhang and Li in 2012 proved that such graphs are planar and admit a Pfaffian orientation. In this article, we describe how to construct graphs with purely imaginary per-spectrum having a subgraph which is an even subdivision of $K_{2,3}$ (planar and nonplanar) using coalescence of rooted graphs. |
| title | A note on graphs with purely imaginary per-spectrum |
| topic | Combinatorics Discrete Mathematics 05C05, 05C31, 05C50, 05C76 G.2.1; G.2.2 |
| url | https://arxiv.org/abs/2211.13072 |