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We present an integer programming model to compute the strong rainbowconnection number, $src(G)$, of any simple graph $G$. We introduce severalenhancements to the proposed model, including a fast heuristic, and a variableelimination scheme. Moreover, we present a novel lower bound for $src(G)$ whichmay be of independent research interest. We solve the integer program bothdirectly and using an alternative method based on iterative lower boundimprovement, the latter of which we show to be highly effective in practice. Toour knowledge, these are the first computational methods for the strong rainbowconnection problem. We demonstrate the efficacy of our methods by computing thestrong rainbow connection numbers of graphs containing up to $379$ vertices.

An integer program and new lower bounds for computing the strong rainbow connection numbers of graphs