On a novel connectivity index. (English) Zbl 1197.92060
Summary: We present a novel connectivity index for (molecular) graphs, called sum-connectivity index and give several basic properties for this index, especially lower and upper bounds in terms of graph (structural) invariants. It appears that this and the original Randić connectivity index that we call product-connectivity index are highly intercorrelated molecular descriptors, the value of the correlation coefficient being 0.991 for trees representing lower alkanes. We determine the unique tree with fixed numbers of vertices and pendant vertices with the minimum value of the sum-connectivity index, and trees with the minimum, second minimum and third minimum, and the maximum, second maximum and third maximum values of this index. Additionally, we discuss the properties of this novel connectivity index for a class of trees representing acyclic hydrocarbons.
MSC:
| 92E10 | Molecular structure (graph-theoretic methods, methods of differential topology, etc.) |
| 05C90 | Applications of graph theory |
| 05C40 | Connectivity |
Keywords:
Randić connectivity index; sum-connectivity index; product-connectivity index; Zagreb indices; molecular graphs; lower and upper boundsReferences:
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