Abstract
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.
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