Abstract The vertex-edge Wiener
index is a graph invariant defined as the sum of distances between
vertices and edges of a graph. In this paper, we study the
relation between the first and second vertex-edge Wiener indices
of thorn graph and its parent graph and examine several special
cases of the results. Results are applied to compute the first and
second vertex-edge Wiener indices of thorn stars, Kragujevac
trees, and dendrimers. ![Creative Commons License](https://i.creativecommons.org/l/by/4.0/80x15.png)
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