Volume 56, Number 1, January-February 2022
|Page(s)||115 - 121|
|Published online||07 February 2022|
Computing some role assignments of Cartesian product of graphs
INF, Universidade Federal de Goiás, Goiânia, GO, Brazil
* Corresponding author: firstname.lastname@example.org
Accepted: 23 December 2021
In social networks, a role assignment is such that individuals play the same role, if they relate in the same way to other individuals playing counterpart roles. When a smaller graph models the social roles in a network, this gives rise to the decision problem called r-Role Assignment whether it exists such an assignment of r distinct roles to the vertices of the graph. This problem is known to be NP-complete for any fixed r ≥ 2. The Cartesian product of graphs is one of the most studied operation on graphs and has numerous applications in diverse areas, such as Mathematics, Computer Science, Chemistry and Biology. In this paper, we determine the computational complexity of r-Role Assignment restricted to Cartesian product of graphs, for r = 2, 3. In fact, we show that the Cartesian product of graphs is always 2-role assignable, however the problem of 3-Role Assignment is still NP-complete for this class.
Mathematics Subject Classification: 05C78 / 05C76 / 68Q25 / 05C15
Key words: Role assignment / Cartesian product / computational complexity
© The authors. Published by EDP Sciences, ROADEF, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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