Related papers: Word-representability of co-bipartite graph

A graph $G = (V, E)$ is said to be word-representable if there exists a word $w$ over the alphabet $V$ such that, for any two distinct letters $x, y \in V$, the letters $x$ and $y$ alternate in $w$ if and only if $xy \in E$. A graph is…

A graph $G$ with vertex set $V(G)$ and edge set $E(G)$ is said to be word-representable if there exists a word $w$ over the alphabet $V(G)$ such that, for any two distinct letters $x,y \in V(G)$, the letters $x$ and $y$ alternate in $w$ if…

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 $xyxy\cdots$ (of even or odd length) or a word $yxyx\cdots$ (of even or odd length). A graph $G=(V,E)$ is…

A graph $G=(V,E)$ is word-representable if and only if there exists a word $w$ over the alphabet $V$ such that letters $x$ and $y$, $x\neq y$, alternate in $w$ if and only if $xy\in E$. A split graph is a graph in which the vertices can be…

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 $(x,y)\in E$ for each $x\neq y$. The set of word-representable graphs generalizes several…

A graph $G = (V, E)$ is word-representable if there exists a word $w$ over the alphabet $V$ such that, for any two distinct vertices $x, y \in V$, $xy \in E$ if and only if $x$ and $y$ alternate in $w$. Two letters $x$ and $y$ are said to…

A pair of letters $x$ and $y$ are said to alternate in a word $w$ if, after removing all letters except for the copies of $x$ and $y$ from $w$, the resulting word is of the form $xyxy\ldots$ (of even or odd length) or $yxyx\ldots$ (of even…

The notion of a word-representable graph has been studied in a series of papers in the literature. 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…

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 $xy\in E$. For integers $n>k>0 $, the shift graph $G(n,k)$ is the graph whose vertex set…

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 $xyxy\cdots$ (of even or odd length) or a word $yxyx\cdots$ (of even or odd length). A graph $G=(V,E)$ is…

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 $(x,y)$ is an edge in $E$. Some graphs are word-representable, others are not. It is…

A word-representable graph is a simple graph $G$ which can be represented by a word $w$ over the vertices of $G$ such that any two vertices are adjacent in $G$ if and only if they alternate in $w$. It is known that the class of…

A graph $G=(V,E)$ is word-representable if there exists a word $w$ over the alphabet $V$ such that letters $x$ and $y$, $x\neq y$, alternate in $w$ if and only if $(x,y)\in E$. Halld\'{o}rsson et al.\ have shown that a graph is…

A graph $G=(V,E)$ is a \emph{word-representable graph} if there exists a word $W$ over the alphabet $V$ such that letters $x$ and $y$ alternate in $W$ if and only if $(x,y)\in E$ for each $x\neq y$. In this paper we give an effective…

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 $E$. It is known that any word-representable graph $G$ is…

A graph $G = (V, E)$ is word-representable, if there exists a word w over the alphabet V such that for letters ${x, y} \in V$ , $x$ and $y$ alternate in $w$ if and only if $xy \in E$. In this paper, we prove that any non-empty…

A simple 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 $w$ iff $xy\in E$. Word-representable graphs generalize several important classes of graphs. A graph…

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 $xy\in E$. Word-representable graphs generalize several important classes of graphs such…

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 $xyxy\cdots$ (of even or odd length) or a word of the form $yxyx\cdots$ (of even or…

Word-representable graphs are a class of graphs that can be represented by words, where edges and non-edges are determined by the alternation of letters in those words. Several papers in the literature have explored the…