On Sombor index of graphs with a given number of cut-vertices
Abstract
Introduced by Gutman in 2021, the Sombor index is a novel graph-theoretic topological descriptor possessing potential applications in the modeling of thermodynamic properties of compounds. Let G^k_n be the set of all n-vertex connected graphs with k cut-vertices. In this paper, we present minimum Sombor indices of graphs in G^k_n. The corresponding extremal graphs have been characterized as well.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2022
- DOI:
- arXiv:
- arXiv:2203.08438
- Bibcode:
- 2022arXiv220308438H
- Keywords:
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- Mathematics - Combinatorics;
- 05C92;
- 05C09;
- 05C35
- E-Print:
- The paper was reviewed by a journal and reviewers found some majors errors in the proofs of results regarding trees in Section 2. Moreover, there was a major error in Lemma 3 of Section 3. Since the main results are based on these lemmas, we need to withdraw the paper from arxive and fix all the errors as it will take a considerable aount of time