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: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Taylor & Francis Group
2022-09-01
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| Series: | AKCE International Journal of Graphs and Combinatorics |
| Subjects: | |
| Online Access: | https://www.tandfonline.com/doi/10.1080/09728600.2022.2093686 |
| Summary: | 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. |
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| ISSN: | 0972-8600 2543-3474 |