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Department of Mathematics, Savitribai Phule Pune University, Pune-411007, India.
10.22061/jdma.2025.11904.1126
Abstract
Let $G$ be a simple graph. In this paper we prove the stated conjecture in [Some notes on Sombor index of graphs, MATCH Commun. Math. Comput. Chem.93 (2025) 853-859] and state an upper bound for the Sombor index of $G$ in terms of its size and the smallest eigenvalue of its Sombor matrix. Also, characterize all graphs for which the specified bound is attained.
Habibi, M. and Singh, R. (2025). Proof of a conjecture on Sombor index. Journal of Discrete Mathematics and Its Applications, 10(2), 157-160. doi: 10.22061/jdma.2025.11904.1126
MLA
Habibi, M. , and Singh, R. . "Proof of a conjecture on Sombor index", Journal of Discrete Mathematics and Its Applications, 10, 2, 2025, 157-160. doi: 10.22061/jdma.2025.11904.1126
HARVARD
Habibi, M., Singh, R. (2025). 'Proof of a conjecture on Sombor index', Journal of Discrete Mathematics and Its Applications, 10(2), pp. 157-160. doi: 10.22061/jdma.2025.11904.1126
CHICAGO
M. Habibi and R. Singh, "Proof of a conjecture on Sombor index," Journal of Discrete Mathematics and Its Applications, 10 2 (2025): 157-160, doi: 10.22061/jdma.2025.11904.1126
VANCOUVER
Habibi, M., Singh, R. Proof of a conjecture on Sombor index. Journal of Discrete Mathematics and Its Applications, 2025; 10(2): 157-160. doi: 10.22061/jdma.2025.11904.1126
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