The Optimal Graph Whose Least Eigenvalue is Minimal among All Graphs via 1-2 Adjacency Matrix
All graphs under consideration are finite, simple, connected, and undirected. Adjacency matrix of a graph G is 0,1 matrix A=aij=0, if vi=vj or dvi,vj≥21, if dvi,vj=1.. Here in this paper, we discussed new type of adjacency matrix known by 1-2 adjacency matrix defined as A1,2G=aij=0, if vi=vj or d...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/8016237 |
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| _version_ | 1832550510775762944 |
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| author | Lubna Gul Gohar Ali Usama Waheed Nudrat Aamir |
| author_facet | Lubna Gul Gohar Ali Usama Waheed Nudrat Aamir |
| author_sort | Lubna Gul |
| collection | DOAJ |
| description | All graphs under consideration are finite, simple, connected, and undirected. Adjacency matrix of a graph G is 0,1 matrix A=aij=0, if vi=vj or dvi,vj≥21, if dvi,vj=1.. Here in this paper, we discussed new type of adjacency matrix known by 1-2 adjacency matrix defined as A1,2G=aij=0, if vi=vj or dvi,vj≥31, if dvi,vj=2, from eigenvalues of the graph, we mean eigenvalues of the 1-2 adjacency matrix. Let Tnc be the set of the complement of trees of order n. In this paper, we characterized a unique graph whose least eigenvalue is minimal among all the graphs in Tnc. |
| format | Article |
| id | doaj-art-acca7c0a1b7b47e7b927ec7529ec8b2b |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-acca7c0a1b7b47e7b927ec7529ec8b2b2025-02-03T06:06:33ZengWileyJournal of Mathematics2314-47852021-01-01202110.1155/2021/8016237The Optimal Graph Whose Least Eigenvalue is Minimal among All Graphs via 1-2 Adjacency MatrixLubna Gul0Gohar Ali1Usama Waheed2Nudrat Aamir3Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of Basic Science and HumanitiesAll graphs under consideration are finite, simple, connected, and undirected. Adjacency matrix of a graph G is 0,1 matrix A=aij=0, if vi=vj or dvi,vj≥21, if dvi,vj=1.. Here in this paper, we discussed new type of adjacency matrix known by 1-2 adjacency matrix defined as A1,2G=aij=0, if vi=vj or dvi,vj≥31, if dvi,vj=2, from eigenvalues of the graph, we mean eigenvalues of the 1-2 adjacency matrix. Let Tnc be the set of the complement of trees of order n. In this paper, we characterized a unique graph whose least eigenvalue is minimal among all the graphs in Tnc.http://dx.doi.org/10.1155/2021/8016237 |
| spellingShingle | Lubna Gul Gohar Ali Usama Waheed Nudrat Aamir The Optimal Graph Whose Least Eigenvalue is Minimal among All Graphs via 1-2 Adjacency Matrix Journal of Mathematics |
| title | The Optimal Graph Whose Least Eigenvalue is Minimal among All Graphs via 1-2 Adjacency Matrix |
| title_full | The Optimal Graph Whose Least Eigenvalue is Minimal among All Graphs via 1-2 Adjacency Matrix |
| title_fullStr | The Optimal Graph Whose Least Eigenvalue is Minimal among All Graphs via 1-2 Adjacency Matrix |
| title_full_unstemmed | The Optimal Graph Whose Least Eigenvalue is Minimal among All Graphs via 1-2 Adjacency Matrix |
| title_short | The Optimal Graph Whose Least Eigenvalue is Minimal among All Graphs via 1-2 Adjacency Matrix |
| title_sort | optimal graph whose least eigenvalue is minimal among all graphs via 1 2 adjacency matrix |
| url | http://dx.doi.org/10.1155/2021/8016237 |
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