ON THE GIRTH, INDEPENDENCE NUMBER, AND WIENER INDEX OF COPRIME GRAPH OF DIHEDRAL GROUP
The coprime graph of a finite group , denoted by , is a graph with vertex set such that two distinct vertices and are adjacent if and only if their orders are coprime, i.e., where |x| is the order of x. In this paper, we complete the form of the coprime graph of a dihedral group that was g...
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Universitas Pattimura
2023-09-01
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| Series: | Barekeng |
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| Online Access: | https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/8905 |
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| author | Agista Surya Bawana Aluysius Sutjijana Yeni Susanti |
| author_facet | Agista Surya Bawana Aluysius Sutjijana Yeni Susanti |
| author_sort | Agista Surya Bawana |
| collection | DOAJ |
| description | The coprime graph of a finite group , denoted by , is a graph with vertex set such that two distinct vertices and are adjacent if and only if their orders are coprime, i.e., where |x| is the order of x. In this paper, we complete the form of the coprime graph of a dihedral group that was given by previous research and it has been proved that if , for some and if . Moreover, we prove that if is even, then the independence number of is , where is the greatest odd divisor of and if is odd, then the independence number of is . Furthermore, the Wiener index of coprime graph of dihedral group has been stated here. |
| format | Article |
| id | doaj-art-ecee9fedc4ae4e7da32c50fcac9e5426 |
| institution | Kabale University |
| issn | 1978-7227 2615-3017 |
| language | English |
| publishDate | 2023-09-01 |
| publisher | Universitas Pattimura |
| record_format | Article |
| series | Barekeng |
| spelling | doaj-art-ecee9fedc4ae4e7da32c50fcac9e54262025-08-20T04:00:55ZengUniversitas PattimuraBarekeng1978-72272615-30172023-09-011731695170210.30598/barekengvol17iss3pp1695-17028905ON THE GIRTH, INDEPENDENCE NUMBER, AND WIENER INDEX OF COPRIME GRAPH OF DIHEDRAL GROUPAgista Surya Bawana0Aluysius Sutjijana1Yeni Susanti2Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Gadjah Mada, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Science, Universitas Gadjah Mada, IndonesiaDepartment of Mathematics, Faculty of Mathematics and Natural Science, Universitas Gadjah Mada, IndonesiaThe coprime graph of a finite group , denoted by , is a graph with vertex set such that two distinct vertices and are adjacent if and only if their orders are coprime, i.e., where |x| is the order of x. In this paper, we complete the form of the coprime graph of a dihedral group that was given by previous research and it has been proved that if , for some and if . Moreover, we prove that if is even, then the independence number of is , where is the greatest odd divisor of and if is odd, then the independence number of is . Furthermore, the Wiener index of coprime graph of dihedral group has been stated here.https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/8905dihedral groupscoprime graphgirthindependence numberwiener index |
| spellingShingle | Agista Surya Bawana Aluysius Sutjijana Yeni Susanti ON THE GIRTH, INDEPENDENCE NUMBER, AND WIENER INDEX OF COPRIME GRAPH OF DIHEDRAL GROUP Barekeng dihedral groups coprime graph girth independence number wiener index |
| title | ON THE GIRTH, INDEPENDENCE NUMBER, AND WIENER INDEX OF COPRIME GRAPH OF DIHEDRAL GROUP |
| title_full | ON THE GIRTH, INDEPENDENCE NUMBER, AND WIENER INDEX OF COPRIME GRAPH OF DIHEDRAL GROUP |
| title_fullStr | ON THE GIRTH, INDEPENDENCE NUMBER, AND WIENER INDEX OF COPRIME GRAPH OF DIHEDRAL GROUP |
| title_full_unstemmed | ON THE GIRTH, INDEPENDENCE NUMBER, AND WIENER INDEX OF COPRIME GRAPH OF DIHEDRAL GROUP |
| title_short | ON THE GIRTH, INDEPENDENCE NUMBER, AND WIENER INDEX OF COPRIME GRAPH OF DIHEDRAL GROUP |
| title_sort | on the girth independence number and wiener index of coprime graph of dihedral group |
| topic | dihedral groups coprime graph girth independence number wiener index |
| url | https://ojs3.unpatti.ac.id/index.php/barekeng/article/view/8905 |
| work_keys_str_mv | AT agistasuryabawana onthegirthindependencenumberandwienerindexofcoprimegraphofdihedralgroup AT aluysiussutjijana onthegirthindependencenumberandwienerindexofcoprimegraphofdihedralgroup AT yenisusanti onthegirthindependencenumberandwienerindexofcoprimegraphofdihedralgroup |