Abstract
The computational complexity of the Hosoya index of a given graph is NP-Complete. Let [Formula: see text] be the graph constructed from [Formula: see text] by a triangle instead of all vertices of the initial graph [Formula: see text]. In this paper, we characterize the Hosoya index of the graph [Formula: see text]. To our surprise, it shows that the Hosoya index of [Formula: see text] is thoroughly given by the order and degrees of all the vertices of the initial graph [Formula: see text].
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