Words for the Graphs with Permutation-Representation Number at most Three
Discrete Mathematics
2023-10-03 v2 Combinatorics
Abstract
The graphs with permutation-representation number (\textit{prn}) at most two are known. While a characterization for the class of graphs with the \textit{prn} at most three is an open problem, we summarize the graphs of this class that are known so far. Although it is known that the \textit{prn} of trees is at most three, in this work, we devise a polynomial-time algorithm for obtaining a word representing a given tree permutationally. Consequently, we determine the words representing even cycles. Contributing to the class of graphs with the \textit{prn} at most three, we determine the \textit{prn} as well as the representation number of book graphs.
Cite
@article{arxiv.2307.00301,
title = {Words for the Graphs with Permutation-Representation Number at most Three},
author = {Khyodeno Mozhui and K. V. Krishna},
journal= {arXiv preprint arXiv:2307.00301},
year = {2023}
}