Minimum sum-connectivity indices of trees and unicyclic graphs of a given matching number. (English) Zbl 1197.92055
Summary: 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 the 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 \(n \geq 4\).
MSC:
| 92E10 | Molecular structure (graph-theoretic methods, methods of differential topology, etc.) |
| 05C07 | Vertex degrees |
| 05C90 | Applications of graph theory |
Keywords:
Randić connectivity index; sum-connectivity index; product-connectivity index; trees; unicyclic graphs; matching numberReferences:
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