Word-representability of Toeplitz graphs
Cheon, Gi-Sang and Kitaev, Sergey and Kim, Jinha and Kim, Minki (2019) Word-representability of Toeplitz graphs. Discrete Applied Mathematics, 270. pp. 96-105. ISSN 0166-218X
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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.
Creators(s): |
Cheon, Gi-Sang, Kitaev, Sergey ![]() | Item type: | Article |
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ID code: | 68963 |
Keywords: | Toeplitz graph, word-representable graph, Riordan graph, pattern, Electronic computers. Computer science, Computer Science(all) |
Subjects: | Science > Mathematics > Electronic computers. Computer science |
Department: | Faculty of Science > Computer and Information Sciences |
Depositing user: | Pure Administrator |
Date deposited: | 22 Jul 2019 14:36 |
Last modified: | 01 Jan 2021 13:10 |
Related URLs: | |
URI: | https://strathprints.strath.ac.uk/id/eprint/68963 |
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