Extremal properties of reciprocal complementary Wiener number of trees. (English) Zbl 1228.05140
Summary: The reciprocal complementary Wiener (RCW) number of a connected graph \(G\) is defined in mathematical chemistry as the sum of the weights \(\frac{1}{d+1-d_G(u,v)}\) of all unordered pairs of distinct vertices, where \(d\) is the diameter and \(d_{G}(u,v)\) is the distance between vertices \(u\) and \(v\) in \(G\). Among others, we characterize the trees of fixed number of vertices and matching number with the smallest RCW number, and the trees that are not caterpillars on \(n\geq 7\) vertices with the smallest, the second-smallest and the third-smallest RCW numbers.
MSC:
| 05C12 | Distance in graphs |
| 05C05 | Trees |
| 05C90 | Applications of graph theory |
| 92E10 | Molecular structure (graph-theoretic methods, methods of differential topology, etc.) |
Keywords:
Wiener number; reciprocal complementary Wiener number; RCW number; distance; tree; caterpillar; matching numberReferences:
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