Extremal unicyclic graphs with fixed leaves via Sombor index

Abstract

Gutman presented the Sombor index in 2021 as a topological molecular descriptor defined by graph A = Σa a ∈E(A) b(a1) +b(a2 ) , where 1 b(a ) is the degree of the vertex 1 a ∈A. A connected graph is said to be unicyclic graph if it has same order and size. In this paper, we characterize the extremal graphs with respect to Sombor index in the class of unicyclic graphs having fixed leaves (nodes with degree one) associated with extremal graphs. Moreover, we compute the bounds on Sombor index in the same class of graphs.