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The Extremal Trees for Logarithmic VDB Topological Indices
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Version 1
: Received: 19 August 2024 / Approved: 19 August 2024 / Online: 20 August 2024 (03:18:35 CEST)
How to cite: Su, Z.; Deng, H. The Extremal Trees for Logarithmic VDB Topological Indices. Preprints 2024, 2024081333. https://doi.org/10.20944/preprints202408.1333.v1 Su, Z.; Deng, H. The Extremal Trees for Logarithmic VDB Topological Indices. Preprints 2024, 2024081333. https://doi.org/10.20944/preprints202408.1333.v1
Abstract
Vertex-degree-based (VDB) topological indices have been applied in QSPR/QSAR. As an important category, the general logarithmic VDB topological index $T_{lnf}(G)$, is defined as the summation of $ln{f(d(u),d(v))}$, where the summation over all $uv\in E(G)$.
In this paper, we give the sufficient conditions for that
(1) the path $P_{n}$ is the only tree with the minimal $T_{lnf}$;
(2) the star $S_n$ is the only tree with the maximal and the minimal $T_{lnf}$, respectively. As applications, the minimal and maximal trees of some logarithmic VDB indices are determined.
Keywords
tree; extreme value; logarithmic VDB topological indices
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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