# On the representation number of a crown graph

@article{Glen2018OnTR, title={On the representation number of a crown graph}, author={Marc Glen and Sergey Kitaev and Artem V. Pyatkin}, journal={Discret. Appl. Math.}, year={2018}, volume={244}, pages={89-93} }

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 $k$-word-representable for some $k$, that is, there exists a word $w$ representing $G$ such that each letter occurs exactly $k$ times in $w$. The minimum such $k$ is called $G$'s representation number.
A crown graph $H_{n,n}$ is a graph obtained from the complete… Expand

#### 5 Citations

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A graph is called $k$-representable if there exists a word $w$ over the nodes of the graph, each node occurring exactly $k$ times, such that there is an edge between two nodes $x,y$ if and only after… Expand

On the Representation Number of Bipartite Graphs

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A polynomial time relabeling algorithm is proposed to produce a word representing a given bipartite graph which is a concatenation of permutations of the graph’s vertices, which gives an upper bound for the representation number of bipartites. Expand

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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… Expand

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In this paper, we compute the regularity and Hilbert series of symbolic powers of cover ideal of a graph G when G is either a crown graph or a complete multipartite graph. We also compute the… Expand

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