Abstract
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 |V(G)|=|E(G)|. Recently, the Sombor index, which is defined bySO=SO(G)=∑uv∈E(G)dG2(u)+dG2(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.
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