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We present formulas to compute the P3-geodetic number, the P3-hull number andthe percolation time for a caterpillar, in terms of certain sequencesassociated with it. In addition, we find a connection between the percolationtime of a unit interval graph and a parameter involving the diameter of a unitinterval graph related to it. Finally, we present a hereditary graph class,defined by forbidden induced subgraphs, such that its percolation time is equalto one.

Formulas in connection with parameters related to convexity of paths on three vertices: caterpillars and unit interval graphs