Azarbaijan Shahid Madani University Communications in Combinatorics and Optimization 2538-2128 Articles in Press 2025 09 12 Characterization of word-representable graphs using modular decomposition 15016 10.22049/cco.2025.30487.2494 EN Tithi Dwary Department of Mathematics, Indian Institute of Technology Guwahati, India K.V. Krishna Department of Mathematics, Indian Institute of Technology Guwahati, India Journal Article 2025 04 02 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 subgraphs induced by modules and the representation number of the associated quotient graph. In this context, 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. https://comb-opt.azaruniv.ac.ir/article_15016_2ae32486c1b1f468c57ba5b804bec162.pdf