Minimum sum-connectivity indices of trees and unicyclic graphs of a given matching number

摘要

The sum-connectivity index is a newly proposed molecular descriptor defined as the sum of the weights of the edges of the graph, where the weight of an edge uv of the graph, incident to vertices u and v, having degrees d _u and d _v is (d _u + d _v )−1/2. We obtain the minimum sum-connectivity indices of trees and unicyclic graphs with given number of vertices and matching number, respectively, and determine the corresponding extremal graphs. Additionally, we deduce the n-vertex unicyclic graphs with the first and second minimum sum-connectivity indices for n ≥ 4. Keywords Randić connectivity index - Sum-connectivity index - Product-connectivity index - Trees - Unicyclic graphs - Matching number