Name
Abstract | ||
|---|---|---|
Based on elementary geometry, Gutman proposed a novel graph invariants called the Sombor index SO(G), which is defined as SO(G) = Sigma(uv epsilon E(G))root d(G(u))(2) + d(G(v))(2), where d(G) (u) and d(G)(v) denote the degree of u and v in G, respectively. It has been proved that the Sombor index could predict some physicochemical properties. In this paper, we characterize the extremal graphs with respect to the Sombor index among all the n-order trees with a given diameter. Firstly, we order the trees with respect to the Sombor index among the n-vertex trees with diameter 3. Then, we determine the largest and the second largest Sombor indices of n-vertex trees with a given diameter d >= 4 and characterize the corresponding trees. Moreover, for n - d = 3, we characterize the extremal n-order trees which reach from the third to the fourth (resp. the sixth, the seventh) largest Sombor indices with d = 4 (resp. d = 5, d >= 6). For n - d >= 4, we characterize the extremal n-order trees which reach from the third to the fifth (resp. the eighth, the ninth) largest Sombor indices with d = 4 (resp. d = 5, d >= 6). As consequences, the top four n-order trees with respect to the Sombor index are characterized. (C) 2021 Elsevier Inc. All rights reserved. |
Year | DOI | Venue |
|---|---|---|
2022 | 10.1016/j.amc.2021.126731 | APPLIED MATHEMATICS AND COMPUTATION |
Keywords | DocType | Volume |
Sombor index, Tree, Diameter, Diametrical path | Journal | 416 |
ISSN | Citations | PageRank |
0096-3003 | 0 | 0.34 |
References | Authors | |
0 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Shuchao Li | 1 | 183 | 35.15 |
| Zheng Wang | 2 | 0 | 0.34 |
| Minjie Zhang | 3 | 0 | 0.68 |