Minimum general sum-connectivity index of unicyclic graphs

摘要

The general sum-connectivity index of a graph G is defined as χ _α (G) = ∑_edges (d _u + d _v ) α , where d _u denotes the degree of vertex u in G and α is a real number. In this report, we determine the minimum and the second minimum values of the general sum-connectivity indices of n-vertex unicyclic graphs for non-zero α ≥ −1, and characterize the corresponding extremal graphs.