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Characterization of word-representable graphs using modular decomposition | ||
Communications in Combinatorics and Optimization | ||
مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 21 شهریور 1404 اصل مقاله (397.43 K) | ||
نوع مقاله: Original paper | ||
شناسه دیجیتال (DOI): 10.22049/cco.2025.30487.2494 | ||
نویسندگان | ||
Tithi Dwary* ؛ K.V. Krishna | ||
Department of Mathematics, Indian Institute of Technology Guwahati, India | ||
چکیده | ||
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. | ||
کلیدواژهها | ||
Word-representable graphs؛ representation number؛ comparability graphs؛ lexicographical product؛ modular decomposition | ||
مراجع | ||
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