Abstract
The strong nonsplit domination polynomial of a graph [Formula: see text] of order [Formula: see text] is the polynomial [Formula: see text], where [Formula: see text] is the number of strong nonsplit dominating sets of [Formula: see text] of size [Formula: see text] and [Formula: see text] is the strong nonsplit domination number of [Formula: see text]. We obtain some properties of [Formula: see text] and its coefficients. Also, we compute the polynomial for some specific graphs.
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