The spectral radius of signless Laplacian matrix and sum-connectivity index of graphs
AbstractThe sum-connectivity index of a graph G is defined as the sum of weights [Formula: see text] over all edges uv of G, where du and dv are the degrees of the vertices u and v in G, respectively. The sum-connectivity index is one of the most important indices in chemical and mathematical fields...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2022-09-01
|
| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/09728600.2022.2093686 |
| _version_ | 1797985354445225984 |
|---|---|
| author | A. Jahanbani S. M. Sheikholeslami |
| author_facet | A. Jahanbani S. M. Sheikholeslami |
| author_sort | A. Jahanbani |
| collection | DOAJ |
| description | AbstractThe sum-connectivity index of a graph G is defined as the sum of weights [Formula: see text] over all edges uv of G, where du and dv are the degrees of the vertices u and v in G, respectively. The sum-connectivity index is one of the most important indices in chemical and mathematical fields. The spectral radius of a square matrix M is the maximum among the absolute values of the eigenvalues of M. Let q(G) be the spectral radius of the signless Laplacian matrix [Formula: see text] where D(G) is the diagonal matrix having degrees of the vertices on the main diagonal and A(G) is the (0, 1) adjacency matrix of G. The sum-connectivity index of a graph G and the spectral radius of the matrix Q(G) have been extensively studied. We investigate the relationship between the sum-connectivity index of a graph G and the spectral radius of the matrix Q(G). We prove that for some connected graphs with n vertices and m edges, [Graphic: see text]q(G)SCI(G)≤n(n+2mn−1−2)n(n−1)+2m−2n+2. |
| first_indexed | 2024-04-11T07:16:52Z |
| format | Article |
| id | doaj.art-7c44388ceb794271b1248b8ea978271f |
| institution | Directory Open Access Journal |
| issn | 0972-8600 2543-3474 |
| language | English |
| last_indexed | 2024-04-11T07:16:52Z |
| publishDate | 2022-09-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | AKCE International Journal of Graphs and Combinatorics |
| spelling | doaj.art-7c44388ceb794271b1248b8ea978271f2022-12-22T04:37:56ZengTaylor & Francis GroupAKCE International Journal of Graphs and Combinatorics0972-86002543-34742022-09-0119319119610.1080/09728600.2022.2093686The spectral radius of signless Laplacian matrix and sum-connectivity index of graphsA. Jahanbani0S. M. Sheikholeslami1Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, IranDepartment of Mathematics, Azarbaijan Shahid Madani University, Tabriz, IranAbstractThe sum-connectivity index of a graph G is defined as the sum of weights [Formula: see text] over all edges uv of G, where du and dv are the degrees of the vertices u and v in G, respectively. The sum-connectivity index is one of the most important indices in chemical and mathematical fields. The spectral radius of a square matrix M is the maximum among the absolute values of the eigenvalues of M. Let q(G) be the spectral radius of the signless Laplacian matrix [Formula: see text] where D(G) is the diagonal matrix having degrees of the vertices on the main diagonal and A(G) is the (0, 1) adjacency matrix of G. The sum-connectivity index of a graph G and the spectral radius of the matrix Q(G) have been extensively studied. We investigate the relationship between the sum-connectivity index of a graph G and the spectral radius of the matrix Q(G). We prove that for some connected graphs with n vertices and m edges, [Graphic: see text]q(G)SCI(G)≤n(n+2mn−1−2)n(n−1)+2m−2n+2.https://www.tandfonline.com/doi/10.1080/09728600.2022.2093686Sum-connectivity indexspectral radiussignless Laplacian matrix05C50 |
| spellingShingle | A. Jahanbani S. M. Sheikholeslami The spectral radius of signless Laplacian matrix and sum-connectivity index of graphs AKCE International Journal of Graphs and Combinatorics Sum-connectivity index spectral radius signless Laplacian matrix 05C50 |
| title | The spectral radius of signless Laplacian matrix and sum-connectivity index of graphs |
| title_full | The spectral radius of signless Laplacian matrix and sum-connectivity index of graphs |
| title_fullStr | The spectral radius of signless Laplacian matrix and sum-connectivity index of graphs |
| title_full_unstemmed | The spectral radius of signless Laplacian matrix and sum-connectivity index of graphs |
| title_short | The spectral radius of signless Laplacian matrix and sum-connectivity index of graphs |
| title_sort | spectral radius of signless laplacian matrix and sum connectivity index of graphs |
| topic | Sum-connectivity index spectral radius signless Laplacian matrix 05C50 |
| url | https://www.tandfonline.com/doi/10.1080/09728600.2022.2093686 |
| work_keys_str_mv | AT ajahanbani thespectralradiusofsignlesslaplacianmatrixandsumconnectivityindexofgraphs AT smsheikholeslami thespectralradiusofsignlesslaplacianmatrixandsumconnectivityindexofgraphs AT ajahanbani spectralradiusofsignlesslaplacianmatrixandsumconnectivityindexofgraphs AT smsheikholeslami spectralradiusofsignlesslaplacianmatrixandsumconnectivityindexofgraphs |