Characterization of Graphs with an Eigenvalue of Large Multiplicity
Let G be a simple and undirected graph. The eigenvalues of the adjacency matrix of G are called the eigenvalues of G. In this paper, we characterize all the n-vertex graphs with some eigenvalue of multiplicity n−2 and n−3, respectively. Moreover, as an application of the main result, we present a fa...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2020/3054672 |
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| _version_ | 1832550994171396096 |
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| author | Linming Qi Lianying Miao Weiliang Zhao Lu Liu |
| author_facet | Linming Qi Lianying Miao Weiliang Zhao Lu Liu |
| author_sort | Linming Qi |
| collection | DOAJ |
| description | Let G be a simple and undirected graph. The eigenvalues of the adjacency matrix of G are called the eigenvalues of G. In this paper, we characterize all the n-vertex graphs with some eigenvalue of multiplicity n−2 and n−3, respectively. Moreover, as an application of the main result, we present a family of nonregular graphs with four distinct eigenvalues. |
| format | Article |
| id | doaj-art-9d61cd5bc00b4e929edce15379398d23 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-9d61cd5bc00b4e929edce15379398d232025-02-03T06:05:16ZengWileyAdvances in Mathematical Physics1687-91201687-91392020-01-01202010.1155/2020/30546723054672Characterization of Graphs with an Eigenvalue of Large MultiplicityLinming Qi0Lianying Miao1Weiliang Zhao2Lu Liu3Department of Fundamental Courses, Zhejiang Industry Polytechnic College, Shaoxing, Zhejiang 312000, ChinaSchool of Mathematics, China University of Mining and Technology, Xuzhou, Jiangsu 221116, ChinaDepartment of Fundamental Courses, Zhejiang Industry Polytechnic College, Shaoxing, Zhejiang 312000, ChinaCollege of Economics and Management, Shandong University of Science and Technology, Qingdao, Shandong 266590, ChinaLet G be a simple and undirected graph. The eigenvalues of the adjacency matrix of G are called the eigenvalues of G. In this paper, we characterize all the n-vertex graphs with some eigenvalue of multiplicity n−2 and n−3, respectively. Moreover, as an application of the main result, we present a family of nonregular graphs with four distinct eigenvalues.http://dx.doi.org/10.1155/2020/3054672 |
| spellingShingle | Linming Qi Lianying Miao Weiliang Zhao Lu Liu Characterization of Graphs with an Eigenvalue of Large Multiplicity Advances in Mathematical Physics |
| title | Characterization of Graphs with an Eigenvalue of Large Multiplicity |
| title_full | Characterization of Graphs with an Eigenvalue of Large Multiplicity |
| title_fullStr | Characterization of Graphs with an Eigenvalue of Large Multiplicity |
| title_full_unstemmed | Characterization of Graphs with an Eigenvalue of Large Multiplicity |
| title_short | Characterization of Graphs with an Eigenvalue of Large Multiplicity |
| title_sort | characterization of graphs with an eigenvalue of large multiplicity |
| url | http://dx.doi.org/10.1155/2020/3054672 |
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