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A note on graphs with purely imaginary per-spectrum

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  • Singh, Ranveer
  • Wankhede, Hitesh

Abstract

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 K2,3, 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 K2,3 (planar and nonplanar) using coalescence of rooted graphs.

Suggested Citation

  • Singh, Ranveer & Wankhede, Hitesh, 2024. "A note on graphs with purely imaginary per-spectrum," Applied Mathematics and Computation, Elsevier, vol. 475(C).
    • Handle: RePEc:eee:apmaco:v:475:y:2024:i:c:s0096300324002248
    DOI: 10.1016/j.amc.2024.128754
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    References listed on IDEAS

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    1. van Dam, E.R. & Haemers, W.H., 2002. "Which Graphs are Determined by their Spectrum?," Discussion Paper 2002-66, Tilburg University, Center for Economic Research.
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