On the Maximum Symmetric Division Deg Index of k-Cyclic Graphs
Let G be a graph. Denote by du, the degree of a vertex u of G and represent by vw, the edge of G with the end-vertices v and w. The sum of the quantities du2+dv2du−1dv−1 over all edges uv of G is known as the symmetric division deg (SDD) index of G. A connected graph with n vertices and n−1+k edges...
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| Format: | Article |
| Language: | English |
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Wiley
2022-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2022/7783128 |
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| author | Abeer M. Albalahi Akbar Ali |
| author_facet | Abeer M. Albalahi Akbar Ali |
| author_sort | Abeer M. Albalahi |
| collection | DOAJ |
| description | Let G be a graph. Denote by du, the degree of a vertex u of G and represent by vw, the edge of G with the end-vertices v and w. The sum of the quantities du2+dv2du−1dv−1 over all edges uv of G is known as the symmetric division deg (SDD) index of G. A connected graph with n vertices and n−1+k edges is known as a (connected)k-cyclic graph. One of the results proved in this study is that the graph possessing the largest SDD index over the class of all connectedk-cyclic graphs of a fixed order n must have the maximum degree n−1. By utilizing this result, the graphs attaining the largest SDD index over the aforementioned class of graphs are determined for every k=0,1,…,5. Although, the deduced results, for k=0,1,2, are already known, however, they are proved here in a shorter and an alternative way. Also, the deduced results, for k=3,4,5, are new, and they provide answers to two open questions posed in the literature. |
| format | Article |
| id | doaj-art-f6af444bcadc4afba99b37a47e5c13cf |
| institution | Kabale University |
| issn | 2314-4785 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-f6af444bcadc4afba99b37a47e5c13cf2025-02-03T06:13:33ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/7783128On the Maximum Symmetric Division Deg Index of k-Cyclic GraphsAbeer M. Albalahi0Akbar Ali1Department of MathematicsDepartment of MathematicsLet G be a graph. Denote by du, the degree of a vertex u of G and represent by vw, the edge of G with the end-vertices v and w. The sum of the quantities du2+dv2du−1dv−1 over all edges uv of G is known as the symmetric division deg (SDD) index of G. A connected graph with n vertices and n−1+k edges is known as a (connected)k-cyclic graph. One of the results proved in this study is that the graph possessing the largest SDD index over the class of all connectedk-cyclic graphs of a fixed order n must have the maximum degree n−1. By utilizing this result, the graphs attaining the largest SDD index over the aforementioned class of graphs are determined for every k=0,1,…,5. Although, the deduced results, for k=0,1,2, are already known, however, they are proved here in a shorter and an alternative way. Also, the deduced results, for k=3,4,5, are new, and they provide answers to two open questions posed in the literature.http://dx.doi.org/10.1155/2022/7783128 |
| spellingShingle | Abeer M. Albalahi Akbar Ali On the Maximum Symmetric Division Deg Index of k-Cyclic Graphs Journal of Mathematics |
| title | On the Maximum Symmetric Division Deg Index of k-Cyclic Graphs |
| title_full | On the Maximum Symmetric Division Deg Index of k-Cyclic Graphs |
| title_fullStr | On the Maximum Symmetric Division Deg Index of k-Cyclic Graphs |
| title_full_unstemmed | On the Maximum Symmetric Division Deg Index of k-Cyclic Graphs |
| title_short | On the Maximum Symmetric Division Deg Index of k-Cyclic Graphs |
| title_sort | on the maximum symmetric division deg index of k cyclic graphs |
| url | http://dx.doi.org/10.1155/2022/7783128 |
| work_keys_str_mv | AT abeermalbalahi onthemaximumsymmetricdivisiondegindexofkcyclicgraphs AT akbarali onthemaximumsymmetricdivisiondegindexofkcyclicgraphs |