Characterization of Word-Representable Graphs using Modular Decomposition
Combinatorics
2024-12-24 v1 Discrete Mathematics
Abstract
In this work, we characterize the class of word-representable graphs with respect to the modular decomposition. Consequently, we determine the representation number of a word-representable graph in terms of the permutation-representation numbers of the modules and the representation number of the associated quotient graph. In this connection, we also obtain a complete answer to the open problem posed by Kitaev and Lozin on the word-representability of the lexicographical product of graphs.
Cite
@article{arxiv.2412.17648,
title = {Characterization of Word-Representable Graphs using Modular Decomposition},
author = {Tithi Dwary and K. V. Krishna},
journal= {arXiv preprint arXiv:2412.17648},
year = {2024}
}
Comments
Presented at the International Conference on Graph Theory and its Applications, Presidency University, Bangalore, held during 20-22 June, 2024