Abstract
Let G be a graph having the set of edges E(G). Represent by dG(u) the degree of a vertex u of G. The Sombor (SO) index of G is defined as SO(G) = sigma(uv is an element of E(G) )root d(G)(u)(2) + d(G)(v)(2).graph with the same order and size is usually referred to as a (connected) unicyclic graph. This paper reports the characterization of the graphs possessing the first-two maximum values of the SO index in the class of all (connected) unicyclic graphs with a fixed girth and order. The length of a shortest cycle in a graph G is known as the girth of G. A connected