A note on graphs with purely imaginary per-spectrum

Ranveer Singh and Hitesh Wankhede

Applied Mathematics and Computation, 2024, vol. 475, issue C

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.

Keywords: Permanental polynomial; Bipartite graphs; Theta graphs; Coalescence (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:475:y:2024:i:c:s0096300324002248

DOI: 10.1016/j.amc.2024.128754

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