Combinatorics

Discrete mathematics

Graph

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Value (mathematics)

Simple graph

Mathematics

Statistics

Epistemology

World Wide Web

Mathematical analysis

Philosophy

Artificial intelligence

Class (philosophy)

Index (typography)

Molecular graph

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Upper and lower bounds

International Journal of Quantum Chemistry

Based on elementary geometry, a class of novel graph invariants was introduced by Gutman, of which the simplest is the Sombor index SO , defined as , where G = ( V , E ) is a simple graph and d G ( v ) denotes the degree of v in G . In this paper, the chemical importance of the Sombor index is investigated and it is shown that the new index is useful in predicting physico‐chemical properties with high accuracy compared to some well‐established and often used indices. We obtain a sharp upper bound for the Sombor index among all molecular trees with fixed numbers of vertices, and characterize those molecular trees achieving the extremal value. Also, we obtain the extremal values of the reduced Sombor index for molecular trees.

Molecular trees with extremal values of Sombor indices