Abstract
Let [Formula: see text] be a set of vertices of a connected graph [Formula: see text]. The Steiner distance of [Formula: see text] is the minimum size of a connected subgraph of [Formula: see text] containing all the vertices of [Formula: see text]. The sum of all Steiner distances on sets of size [Formula: see text] is called the Steiner [Formula: see text]-Wiener index. A graph [Formula: see text] is modular if for every three vertices [Formula: see text] there exists a vertex [Formula: see text] that lies on the shortest path between every two vertices of [Formula: see text]. The Steiner 3-Wiener index of a modular graph is obtained in terms of its Wiener index. As concrete examples, we discuss the case of Fibonacci, Lucas cubes and the Cartesian product of modular graphs. The Steiner Wiener index of block graphs is also studied.
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