Word-Representability of Graphs with respect to Split Recomposition
CoRR(2024)
摘要
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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