Word-representability of Toeplitz graphs

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Distinct letters x and y alternate in a word w if after deleting in w all letters but the copies of x and y we either obtain a word of the form xyxy ... (of even or odd length) or a word of the form yxyx ... (of even or odd length). A graph G = (V, E) is word-representable if there exists a word w over the alphabet V such that letters x and y alternate in w if and only if xy is an edge in E. In this paper we initiate the study of word-representable Toeplitz graphs, which are Riordan graphs of the Appell type. We prove that several general classes of Toeplitz graphs are word-representable, and we also provide a way to construct non-word-representable Toeplitz graphs. Our work not only merges the theories of Riordan matrices and word-representable graphs via the notion of a Riordan graph, but also it provides the first systematic study of word-representability of graphs defined via patterns in adjacency matrices. Moreover, our paper introduces the notion of an infinite word-representable Riordan graph and gives several general examples of such graphs. It is the first time in the literature when the word-representability of infinite graphs is discussed. (C) 2019 Elsevier B.V. All rights reserved.
Publisher
ELSEVIER
Issue Date
2019-11
Language
English
Article Type
Article
Citation

DISCRETE APPLIED MATHEMATICS, v.270, pp.96 - 105

ISSN
0166-218X
DOI
10.1016/j.dam.2019.07.013
URI
http://hdl.handle.net/10203/268863
Appears in Collection
MT-Journal Papers(저널논문)
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