广泛广义线图覆盖的唯一性
The uniqueness of covers for widely generalized line graphs
摘要：
作为线图的一种自然推广，Hoffman线图是由Woo和Neumaier定义的。特别是Hoffman线图与图的最小特征值密切相关，而Hoffman线图的严格覆盖的唯一性在此类研究中起着关键作用。本文证明了在有限时间内可检验的条件下严格覆盖唯一性的一个定理。我们的结果是[Ars Math.~]主要部分的推广和简短证明对流\textbf{1}（2008）81- 98]。
英文摘要：
As a natural generalization of line graphs, Hoffman line graphs were defined by Woo and Neumaier. Especially, Hoffman line graphs are closely related to the smallest eigenvalue of graphs, and the uniqueness of strict covers of a Hoffman line graph plays a key role in such a study. In this paper, we prove a theorem for the uniqueness of strict covers under a condition which can be checked in finite time. Our result gives a generalization and a short proof for the main part of [Ars Math.~Contemp. \textbf{1} (2008) 81--98].
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