Word-representability of Toeplitz graphs

Gi-Sang Cheon, Sergey Kitaev, Jinha Kim, Minki Kim

Research output: Contribution to journalArticle

Abstract

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.
Language English 1-18 18 Discrete Applied Mathematics Accepted/In press - 21 Jul 2019

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Representability
Otto Toeplitz
Graph in graph theory
Alternate
Odd
Infinite Words
Infinite Graphs
If and only if
Distinct

Keywords

• Toeplitz graph
• word-representable graph
• Riordan graph
• pattern

Cite this

Cheon, G-S., Kitaev, S., Kim, J., & Kim, M. (Accepted/In press). Word-representability of Toeplitz graphs. Discrete Applied Mathematics, 1-18.
Cheon, Gi-Sang ; Kitaev, Sergey ; Kim, Jinha ; Kim, Minki. / Word-representability of Toeplitz graphs. In: Discrete Applied Mathematics. 2019 ; pp. 1-18.
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Word-representability of Toeplitz graphs. / Cheon, Gi-Sang; Kitaev, Sergey; Kim, Jinha; Kim, Minki.

In: Discrete Applied Mathematics, 21.07.2019, p. 1-18.

Research output: Contribution to journalArticle

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