Extremal unicyclic graphs of Sombor index

Unicyclic graph is one kind of typical graph for indices basing degree of vertex. Various chemical structures can be exhibited in unicyclic graph as well. A graph is said to be unicyclic if the graph is connected and vertical bar V(G)vertical bar = vertical bar E(G)vertical bar. Recently, the Sombor index, which is defined by SO = SO(G) = Sigma(uv is an element of E(G)) root d(G)(2)(u) + d(G)(2)(v), was proposed by Gutman. This paper establishes distinct bounds for this index of unicyclic graph with girth l, as well as specific bounds of chemical unicyclic graph with girth l.