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arXiv · 2003.08782

On the largest eigenvalue of a mixed graph with partial orientation

Bo-Jun Yuan·Yi Wang·Yi-Zheng Fan
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Abstract

Let $G$ be a connected graph and let $T$ be a spanning tree of $G$. A partial orientation $σ$ of $G$ respect to $T$ is an orientation of the edges of $G$ except those edges of $T$, the resulting graph associated with which is denoted by $G_T^σ$. In this paper we prove that there exists a partial orientation $σ$ of $G$ respect to $T$ such that the largest eigenvalue of the Hermitian adjacency matrix of $G_T^σ$ is at most the largest absolute value of the roots of the matching polynomial of $G$.

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Bo-Jun Yuan, Yi Wang, Yi-Zheng Fan. 2020-03-18. On the largest eigenvalue of a mixed graph with partial orientation. https://doi.org/10.1016/j.laa.2021.06.003

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