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 H k n be the family of graphs on order n and k number of cutvertices having at least one cycle. In this paper, we present minimum Sombor indices of graphs in H k n. The corresponding extremal graphs have been characterized as well.

Comparative study of Sombor index and its various versions using regression models for top priority polycyclic aromatic hydrocarbons

“…It has been proved that, it holds promise for decoding the thermodynamic behaviour of compounds. Hayat et al, [30] proposed the minimum Sombor index of graphs while Sakandar et al, [31] employed valency-based indices in QSPR studies for monocarboxylic acids for physicochemical properties.…”

Extremal Sombor Index of Graphs with Cut Edges and Clique Number

“…In [8], they showed applications of the Sombor index. For more studies in this direction, one may refer to [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”

Extra Edge Connectivity and Extremal Problems in Education Networks

“…The edge connectivity of Γ, written λ(Γ), is the minimum size of an edge subset M ⊆ E(Γ) such that Γ − M is disconnected. The extremal graphs with respect to various topological descriptors of graphs with given connectivity and edge connectivity have been studied in [4,5] and the references therein. We skip the definitions of other standard graph-theoretical notions, as these can be found in [6] and other textbooks.…”