Optimal inequalities and extremal problems on the general Sombor index
J. C. Hern\'andez, J. M. Rodr\'iguez, O. Rosario, J. M. Sigarreta
TL;DR
This paper establishes new bounds and extremal problems for the general Sombor index, relating it to other graph indices and providing insights into its extremal values.
Contribution
It introduces novel bounds for the general Sombor index and solves extremal problems, connecting it with other well-known graph indices.
Findings
Derived new lower and upper bounds for the general Sombor index.
Established inequalities relating the Sombor index with the Zagreb and forgotten indices.
Solved extremal problems to identify graphs with extremal Sombor index values.
Abstract
In this work we obtain new lower and upper optimal bounds of general Sombor indices. Specifically, we have inequalities for these indices relating them with other indices: the first Zagreb index, the forgotten index and the first variable Zagreb index. Finally, we solve some extremal problems for general Sombor indices.
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Taxonomy
TopicsGraph theory and applications · Synthesis and Properties of Aromatic Compounds · Metal-Organic Frameworks: Synthesis and Applications