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arXiv · 1409.3036

Permanental polynomials of skew adjacency matrices of oriented graphs

Shunyi Liu·Heping Zhang
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Abstract

Let $G^σ$ be an orientation of a simple graph $G$. In this paper, the permanental polynomial of an oriented graph $G^σ$ is introduced. The coefficients of the permanental polynomial of $G^σ$ are interpreted in terms of the graph structure of $G^σ$, and it is proved that all orientations $G^σ$ of $G$ have the same permanental polynomial if and only if $G$ has no even cycles. Furthermore, the roots of the permanental polynomial of $G^σ$ are studied.

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Shunyi Liu, Heping Zhang. 2016-11-17. Permanental polynomials of skew adjacency matrices of oriented graphs. https://doi.org/10.13885/j.issn.0455-2059.2016.05.018

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