Papers
Topics
Authors
Recent
Search
2000 character limit reached

On the Sombor index of trees with degree restrictions

Published 1 Apr 2024 in math.CO | (2404.01442v1)

Abstract: We study the Sombor index of trees with various degree restrictions. In addition to rediscovering that among all trees with a given degree sequence, the greedy tree minimises the Sombor index and the alternating greedy tree maximises it, we also provide a full characterisation of all trees that have those maximum or minimum values. Moreover, we compare trees with different degree sequences and deduce a few corollaries.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (11)
  1. E. O. D. Andriantiana. Energy, hosoya index and merrifield–simmons index of trees with prescribed degree sequence. Discrete Applied Mathematics, 161(6):724–741, 2013.
  2. Extremal values on the sombor index of trees. MATCH Commun. Math. Comput. Chem, 87(2022):87, 2022.
  3. I. Damnjanović and D. Stevanović. Greedy trees have minimum sombor indices. arXiv preprint arXiv:2211.05559, 2022.
  4. I. Gutman. Geometric approach to degree-based topological indices: Sombor indices. MATCH Commun. Math. Comput. Chem, 86(1):11–16, 2021.
  5. On the extremal sombor index of trees with a given diameter. Applied Mathematics and Computation, 416:126731, 2022.
  6. On the sombor index of graphs. Contrib. Math., pages 11–18, 2021.
  7. Greedy trees, Caterpillars, and Wiener-type graph invariants. MATCH Commun. Math. Comput. Chem., 68(1):273–292, 2012.
  8. H. Wang. The extremal values of the Wiener index of a tree with given degree sequence. Discrete Appl. Math., 156(14):2647–2654, 2008.
  9. P. Wei and M. Liu. Note on sombor index of connected graphs with given degree sequence. Discrete Applied Mathematics, 330:51 – 55, 2023.
  10. X.-D. Zhang. The Laplacian spectral radii of trees with degree sequences. Discrete Math., 308(15):3143–3150, 2008.
  11. The number of subtrees of trees with given degree sequence. Journal of Graph Theory, 73(3):280–295, 2013.

Summary

No one has generated a summary of this paper yet.

Sign Up to Summarize

Paper to Video (Beta)

No one has generated a video about this paper yet.

Sign Up to Generate All Videos Subscribe on YouTube

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Generate Now

Collections

Sign up for free to add this paper to one or more collections.

Sign Up

Tweets

Sign up for free to view the 1 tweet with 0 likes about this paper.

Sign Up for Free