| k圈图的最大Laplace分离度 |
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| 引用本文： | 余桂东,阮征,舒阿秀.k圈图的最大Laplace分离度[J].运筹学学报,2022,26(2):137-142. |
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| 作者姓名： | 余桂东 阮征 舒阿秀 |
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| 作者单位： | 1. 安庆师范大学数理学院, 安徽安庆 2461332. 合肥幼儿师范高等专科学校公共教学部, 安徽合肥 230013 |
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| 基金项目： | 国家自然科学基金(11871077);安徽省自然科学基金(1808085MA04);安徽省高校自然科学基金(KJ2020A0894);合肥幼专图论科研创新团队(KCTD202001) |
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| 摘 要： | 设$ G $是一个$ n $阶$ k $圈图, $ k $圈图为边数等于顶点数加$ k-1 $的简单连通图。$ \mu_{1}(G) $、$ \mu_{2}(G) $分别记为图$ G $的Laplace矩阵的最大特征值和次大特征值, 图$ G $的Laplace分离度定义为$ S_{L}(G)=\mu_{1}(G)-\mu_{2}(G) $。本文研究了给定阶数的$ k $圈图的最大Laplace分离度, 并刻画了相应的极图, 其结果推广了已有当$ k=1, 2, 3 $时的结论。
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| 关 键 词： | k圈图 Laplace矩阵 Laplace分离度 |
| 收稿时间： | 2019-01-15 |
The maximum Laplacian separator of $ k $-cyclic graph |
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| Affiliation: | 1. School of Mathematics and Physics, Anqing Normal University, Anqing 246133, Anhui, China2. Department of Public Teaching, Hefei Preschool Education College, Hefei 230013, Anhui, China |
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| Abstract: | Let $ G $ be an $ n $-order $ k $-cyclic graph. The $ k $-cyclic graph is a simply connected graph which the number of edges is equal to the number of vertices adding $ k-1 $. Let $ \mu_{1}(G) $ and $ \mu_{2}(G) $ be the largest eigenvalue and the second largest eigenvalue of the Laplacian matrix of $ G $, respectively. The Laplacian separator of graph $ G $ is defined as $ S_{L}(G)=\mu_{1}(G)-\mu_{2}(G) $. In this paper, we study the maximun Laplacian separator of $ k $-cyclic graph with given order, and characterize the according extremal graph. The result generalizes the existing conclusions when $ k=1, 2, 3 $. |
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| Keywords: | k-cyclic graph Laplacian matrix Laplacian separator |
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