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 is a bipartite graph containing no subgraph which is an even subdivision of , 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 (planar and nonplanar) using coalescence of rooted graphs.

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关于具有纯虚数每光谱的图的注释


1983 年，Borowiecki 和 Jóźwiak 提出了“表征那些具有纯虚构每谱的图”的问题。这个问题仍然悬而未决。最一般的结果，虽然是部分解决方案，由 Yan 和Zhang 在 2004 年给出，他们表明，如果 是一个不包含子图的二分图，它是 的偶数细分，那么它具有纯虚数的每谱。张和李在 2012 年证明了这样的图是平面的并且承认普法夫方向。在本文中，我们描述了如何使用纯虚数每谱构造图，该图具有子图，该子图是使用有根图的合并的（平面和非平面）的均匀细分。