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Trees and their quadratic line graphs having the same Wiener index. (English) Zbl 1052.05029

The Wiener index \(W(G)\) of a graph \(G\) is a topological index and it is defined as the half of the sum of the distances between every pair of vertices of \(G\). The authors find infinite families of chemical trees \(T\) with the property \(W(T)=W(L(L(T)))\), where \(L(G)\) is the line graph of \(G\).

MSC:

05C12 Distance in graphs
05C05 Trees
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