Generating and counting unlabeled k-path graphs

Authors:
Paulo Renato Da Costa Pereira;Alex Garcia;Lilian Markenzon
Affiliations:
Instituto Militar de Engenharia, Praça General Tibúrcio 80, 22290-270, Rio de Janeiro, Brazil;Instituto Militar de Engenharia, Praça General Tibúrcio 80, 22290-270, Rio de Janeiro, Brazil;Núcleo de Computação Eletrônica, Universidade Federal do Rio de Janeiro, CP 2324, 20010-974, Rio de Janeiro, Brazil
Venue:
Discrete Applied Mathematics
Year:
2014

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Abstract

A subfamily of k-trees, the k-path graphs generalize path graphs in the same way k-trees generalize trees. This paper presents a code for unlabeled k-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 k-path graphs with n vertices and generating all elements of the family.