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arXiv · 2412.17648

Characterization of Word-Representable Graphs using Modular Decomposition

Tithi Dwary·K. V. Krishna
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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.

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Tithi Dwary, K. V. Krishna. 2024-12-23. Characterization of Word-Representable Graphs using Modular Decomposition. https://arxiv.org/abs/2412.17648

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