Word-Representability of Graphs with respect to Split Recomposition
Abstract
In this work, we show that the class of word-representable graphs is closed under split recomposition and determine the representation number of the graph obtained by recomposing two word-representable graphs. Accordingly, we show that the class of parity graphs is word-representable. Further, we obtain a characteristic property by which the recomposition of comparability graphs is a comparability graph. Consequently, we also establish the permutation-representation number (prn) of the resulting comparability graph. We also introduce a subclass of comparability graphs, called prn-irreducible graphs. We provide a criterion such that the split recomposition of two prn-irreducible graphs is a comparability graph and determine the prn of the resultant graph.
Cite
@article{arxiv.2401.01954,
title = {Word-Representability of Graphs with respect to Split Recomposition},
author = {Tithi Dwary and K. V. Krishna},
journal= {arXiv preprint arXiv:2401.01954},
year = {2024}
}