Relationship between adjacency and distance matrix of graph of diameter two
The relationship among every pair of vertices in a graph can be represented as a matrix, such as in adjacency matrix and distance matrix. Both adjacency and distance matrices have the same property. Adjacency and distance matrices are both symmetric matrix with diagonals entries equals to 0. In thi...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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InaCombS; Universitas Jember; dan Universitas Indonesia
2021-12-01
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| Series: | Indonesian Journal of Combinatorics |
| Subjects: | |
| Online Access: | http://www.ijc.or.id/index.php/ijc/article/view/55 |
| _version_ | 1828057114575110144 |
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| author | Siti L. Chasanah Elvi Khairunnisa Muhammad Yusuf Kiki A. Sugeng |
| author_facet | Siti L. Chasanah Elvi Khairunnisa Muhammad Yusuf Kiki A. Sugeng |
| author_sort | Siti L. Chasanah |
| collection | DOAJ |
| description | The relationship among every pair of vertices in a graph can be represented as a matrix, such as in adjacency matrix and distance matrix. Both adjacency and distance matrices have the same property. Adjacency and distance matrices are both symmetric matrix with diagonals entries equals to 0. In this paper, we discuss relationships between adjacency matrix and distance matrix of a graph of diameter two, which is <em>D=2(J-I)-A</em>. From this relationship, we also determine the value of the determinant matrix <em>A+D</em> and the upper bound of determinant of matrix <em>D</em>. |
| first_indexed | 2024-04-10T21:07:28Z |
| format | Article |
| id | doaj.art-32bf57525a7d477aa7d7748b6c78f313 |
| institution | Directory Open Access Journal |
| issn | 2541-2205 |
| language | English |
| last_indexed | 2024-04-10T21:07:28Z |
| publishDate | 2021-12-01 |
| publisher | InaCombS; Universitas Jember; dan Universitas Indonesia |
| record_format | Article |
| series | Indonesian Journal of Combinatorics |
| spelling | doaj.art-32bf57525a7d477aa7d7748b6c78f3132023-01-22T03:09:48ZengInaCombS; Universitas Jember; dan Universitas IndonesiaIndonesian Journal of Combinatorics2541-22052021-12-0152636710.19184/ijc.2021.5.2.164Relationship between adjacency and distance matrix of graph of diameter twoSiti L. ChasanahElvi KhairunnisaMuhammad YusufKiki A. SugengThe relationship among every pair of vertices in a graph can be represented as a matrix, such as in adjacency matrix and distance matrix. Both adjacency and distance matrices have the same property. Adjacency and distance matrices are both symmetric matrix with diagonals entries equals to 0. In this paper, we discuss relationships between adjacency matrix and distance matrix of a graph of diameter two, which is <em>D=2(J-I)-A</em>. From this relationship, we also determine the value of the determinant matrix <em>A+D</em> and the upper bound of determinant of matrix <em>D</em>.http://www.ijc.or.id/index.php/ijc/article/view/55adjacency matrix, distance matrix, diameter |
| spellingShingle | Siti L. Chasanah Elvi Khairunnisa Muhammad Yusuf Kiki A. Sugeng Relationship between adjacency and distance matrix of graph of diameter two Indonesian Journal of Combinatorics adjacency matrix, distance matrix, diameter |
| title | Relationship between adjacency and distance matrix of graph of diameter two |
| title_full | Relationship between adjacency and distance matrix of graph of diameter two |
| title_fullStr | Relationship between adjacency and distance matrix of graph of diameter two |
| title_full_unstemmed | Relationship between adjacency and distance matrix of graph of diameter two |
| title_short | Relationship between adjacency and distance matrix of graph of diameter two |
| title_sort | relationship between adjacency and distance matrix of graph of diameter two |
| topic | adjacency matrix, distance matrix, diameter |
| url | http://www.ijc.or.id/index.php/ijc/article/view/55 |
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