On the Minimum Modified Sombor Index of the Unicyclic Graphs by the Restrictions on the Girth

The Modified Sombor Index of a graph G is defined as the reciprocal of the well known Sombor Index. The girth of G, by short g(G), is the length of the smallest cycle in G. A graph with exactly one cycle is a unicyclic graph. If it is further, connected, it is a connected unicyclic graph. In this article, we achieved the minimum and second minimum modified Sombor Index of unicyclic graphs and also found the graphs achieving the minimum and second minimum modified Sombor Index.