A note on extremal Sombor indices of trees with a given degree sequence
Ivan Damnjanovi\'c, Marko Milo\v{s}evi\'c, Dragan Stevanovi\'c
TL;DR
This paper identifies the extremal trees with minimum and maximum Sombor indices among trees with a fixed degree sequence, extending previous results and confirming the optimality of greedy and alternating greedy trees.
Contribution
It establishes the extremal trees for the Sombor index in the context of a given degree sequence, building on and applying existing theoretical frameworks.
Findings
Greedy trees minimize the Sombor index.
Alternating greedy trees maximize the Sombor index.
Results align with previous theoretical frameworks.
Abstract
We note here that the problem of determining extremal values of Sombor index for trees with a given degree sequence fits within the framework of results by Hua Wang from [Cent. Eur. J. Math. 12 (2014) 1656-1663], implying that the greedy tree has the minimum Sombor index, while an alternating greedy tree has the maximum Sombor index.
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Taxonomy
TopicsGraph theory and applications · Advanced Graph Theory Research · Synthesis and Properties of Aromatic Compounds