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arXiv · 2511.22361

The spectral radii and extremal graphs of two types of minimal graphs

Liwen Lian·Jinfeng Liu·Mengyuan Niu·Xiumei Wang
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Abstract

A connected nontrivial graph $G$ is {\it matching covered} if every edge of $G$ is contained in some perfect matching of $G$. A matching covered graph $G$ is {\it minimal} if $G-e$ is not matching covered for each edge $e$ of $G$. A graph is said to be {\it factor-critical} if $G-v$ has a perfect matching for every $v\in V(G)$. A factor-critical graph $G$ is said to be {\it minimal factor-critical} if $G-e$ is not factor-critical graph for each edge $e\in E(G)$. In this paper, by employing ear decomposition and edge-exchange techniques, the greatest spectral radii of minimal matching covered bipartite graphs and minimal factor-critical graphs are determined, and the corresponding extremal graphs are characterized.

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Liwen Lian, Jinfeng Liu, Mengyuan Niu, Xiumei Wang. 2025-11-27. The spectral radii and extremal graphs of two types of minimal graphs. https://arxiv.org/abs/2511.22361

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