Generating and counting unlabeled kk-path graphs

A subfamily of kk-trees, the kk-path graphs generalize path graphs in the same way kk-trees generalize trees. This paper presents a code for unlabeled kk-path graphs. The effect of structural properties of the family on the code is investigated, leading to the solution of two problems: determining the exact number of unlabeled kk-path graphs with nn vertices and generating all elements of the family.