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- Title
The k-Sombor Index of Trees.
- Authors
Wang, Fangxia; Wu, Baoyindureng
- Abstract
For a positive real number k , the k -Sombor index of a graph G , introduced by Réti et al, is defined as SO k (G) = ∑ u v ∈ E (G) d (u) k + d (v) k k , where d (u) denotes the degree of the vertex u in G. By the definition, S O 2 (G) is exactly the Sombor index of G , while S O 1 (G) is the first Zagreb index of G. In this paper, for k ≥ 1 we present the extremal values of the k -Sombor index of trees with some given parameters, such as matching number, the number of pendant vertices, diameter. This generalizes the relevant results on Sombor index due to Chen, Li and Wang ((2002). Extremal values on the Sombor index of trees, MATCH Communications in Mathematical and in Computer Chemistry, 87, 23–49). Handling S O k (G) appears to be different for k < 1 in contrast to the case when k ≥ 1. To demonstrate this, we also characterize the extremal trees with respect to the SO 1 2 with matching number, the number of pendant vertices and diameter. In addition, three relevant conjectures are proposed.
- Subjects
REAL numbers; TREES
- Publication
Asia-Pacific Journal of Operational Research, 2024, Vol 41, Issue 1, p1
- ISSN
0217-5959
- Publication type
Article
- DOI
10.1142/S0217595923500021