Maximal graphs with a prescribed complete bipartite graph as a star complement
Let G be a graph of order n and μ be an adjacency eigenvalue of G with multiplicity k≥1. A star complement for μ in G is an induced subgraph of G of order n−k with no eigenvalue μ. In this paper, we characterize the maximal graphs with the bipartite graph K<sub>2</sub>,s as a star comple...
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| Format: | Article |
| Language: | English |
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AIMS Press
2021-05-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2021419?viewType=HTML |
| _version_ | 1829142721822982144 |
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| author | Xiaona Fang Lihua You Yufei Huang |
| author_facet | Xiaona Fang Lihua You Yufei Huang |
| author_sort | Xiaona Fang |
| collection | DOAJ |
| description | Let G be a graph of order n and μ be an adjacency eigenvalue of G with multiplicity k≥1. A star complement for μ in G is an induced subgraph of G of order n−k with no eigenvalue μ. In this paper, we characterize the maximal graphs with the bipartite graph K<sub>2</sub>,s as a star complement for eigenvalues μ=−2,1 and study the cases of other eigenvalues for further research. |
| first_indexed | 2024-12-14T20:37:39Z |
| format | Article |
| id | doaj.art-94aa3e10a64948adad9cde7a150395aa |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-14T20:37:39Z |
| publishDate | 2021-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-94aa3e10a64948adad9cde7a150395aa2022-12-21T22:48:22ZengAIMS PressAIMS Mathematics2473-69882021-05-01677153716910.3934/math.2021419Maximal graphs with a prescribed complete bipartite graph as a star complementXiaona Fang0Lihua You1Yufei Huang21. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China1. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China2. Department of Mathematics Teaching, Guangzhou Civil Aviation College, Guangzhou, 510403, ChinaLet G be a graph of order n and μ be an adjacency eigenvalue of G with multiplicity k≥1. A star complement for μ in G is an induced subgraph of G of order n−k with no eigenvalue μ. In this paper, we characterize the maximal graphs with the bipartite graph K<sub>2</sub>,s as a star complement for eigenvalues μ=−2,1 and study the cases of other eigenvalues for further research.https://www.aimspress.com/article/doi/10.3934/math.2021419?viewType=HTMLadjacency eigenvaluestar setstar complementmaximal graph |
| spellingShingle | Xiaona Fang Lihua You Yufei Huang Maximal graphs with a prescribed complete bipartite graph as a star complement AIMS Mathematics adjacency eigenvalue star set star complement maximal graph |
| title | Maximal graphs with a prescribed complete bipartite graph as a star complement |
| title_full | Maximal graphs with a prescribed complete bipartite graph as a star complement |
| title_fullStr | Maximal graphs with a prescribed complete bipartite graph as a star complement |
| title_full_unstemmed | Maximal graphs with a prescribed complete bipartite graph as a star complement |
| title_short | Maximal graphs with a prescribed complete bipartite graph as a star complement |
| title_sort | maximal graphs with a prescribed complete bipartite graph as a star complement |
| topic | adjacency eigenvalue star set star complement maximal graph |
| url | https://www.aimspress.com/article/doi/10.3934/math.2021419?viewType=HTML |
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