Word-Representability of Line Graphs

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Word-Representability of Line Graphs

A graph is representable if there exists a word over the alphabet such that letters  = , G V E  W V x and alternate in W if and only if y   , x y is in E for each x not equal to . The motivation to study representable graphs came from algebra, but this subject is interesting from graph theoretical, computer science, and combinatorics on words points of view. In this paper, we prove that for...

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On the Representability of Line Graphs

A graph G = (V,E) is representable if there exists a word W over the alphabet V such that letters x and y alternate in W if and only if (x, y) is in E for each x not equal to y. The motivation to study representable graphs came from algebra, but this subject is interesting from graph theoretical, computer science, and combinatorics on words points of view. In this paper, we prove that for n gre...

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Word-representability of triangulations of grid-covered cylinder graphs

A graph G = (V,E) is word-representable if there exists a word w over the alphabet V such that letters x and y, x 6= y, alternate in w if and only if (x, y) ∈ E. Halldórsson, Kitaev and Pyatkin have shown that a graph is word-representable if and only if it admits a so-called semi-transitive orientation. A corollary of this result is that any 3-colorable graph is wordrepresentable.Masárová Akro...

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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 (x, y) ∈ E. A triangular grid graph is a subgraph of a tiling of the plane with equilateral triangles defined by a finite number of triangles, called cells. A face subdivision of a triangular grid graph is replacing some of its cells by plane copies of the...

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Triangular line graphs and word sense disambiguation

Linguists often represent the relationships between words in a collection of text as an undirected graph G = (V,E), were V is the vocabulary and vertices are adjacent in G if and only if the words they represent co-occur in a relevant pattern in the text. Ideally, the words with similar meanings give rise to the vertices of a component of the graph. However, many words have several distinct mea...

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ژورنال

عنوان ژورنال: Open Journal of Discrete Mathematics

سال: 2011

ISSN: 2161-7635,2161-7643

DOI: 10.4236/ojdm.2011.12012