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arXiv · 2401.01954

Word-Representability of Graphs with respect to Split Recomposition

Tithi Dwary·K. V. Krishna
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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.

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Tithi Dwary, K. V. Krishna. 2024-01-03. Word-Representability of Graphs with respect to Split Recomposition. https://arxiv.org/abs/2401.01954

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