Contents
1 Reconfiguration Graph of Independent Sets under Token Sliding
1.1 Definitions
An independent set $I$ of a graph $G$ is a subset of vertices of $G$ where any two members $u,v\in I$, there is no edge of $G$ connecting $u$ and $v$. The reconfiguration graph of independent sets of $G$ under Token Sliding, denoted by $\U0001d5b3\U0001d5b2(G)$, takes all independent sets of $G$ as its nodes (vertices). Two nodes $I,J$ of $\U0001d5b3\U0001d5b2(G)$ are adjacent if there are two vertices $u,v$ such that $I\setminus J=\{u\}$, $J\setminus I=\{v\}$, and $uv$ is an edge of $G$.
1.2 Graph Data

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The first line of the file contains the number of graphs, followed by a blank line.

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For each graph $H$, if $H=\U0001d5b3\U0001d5b2(G)$ is nonplanar for some graph $G$, we provide data on a Kuratowski subgraph of $H$, not the whole graph $H$.

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For each graph:

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The first line contains the number of vertices $n$.

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Each of the next $n$ lines is of the form:
vertex: label
. Thevertex
is counted from $0$ to $n1$.If the graph is planar, the format is
vertex: label: x y
, where $x$ and $y$ are the coordinates of the vertex in a planar layout of the graph.If the graph is $\U0001d5b3\U0001d5b2(G)$ for some graph $G$, the
label
is of the form[v1, v2, ..., vk]
, which represents a size$k$ independent set of $G$. 
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The next $n$ lines describe the corresponding adjacency matrix.

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The description ends by a blank line.

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$n$  $G$  $\U0001d5b3\U0001d5b2(G)$  

connected planar  tree  path  cycle  
$G$  $\U0001d5b3\U0001d5b2(G)$  $G$  $\U0001d5b3\U0001d5b2(G)$  $G$  $\U0001d5b3\U0001d5b2(G)$  $G$  $\U0001d5b3\U0001d5b2(G)$  
$n=6$  99  99  6  6  1  1  1  1  planar 
0  0  0  0  0  0  0  0  nonplanar  
$n=7$  584  584  11  11  1  1  0  0  planar 
62  62  0  0  0  0  1  1  nonplanar  
$n=8$  3145  3145  16  16  1  1  0  0  planar 
2829  2829  7  7  0  0  1  1  nonplanar  
$n=9$  7863  7863  12  12  0  0  0  0  planar 
64022  64022  35  35  1  1  1  1  nonplanar 
History

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2021/07/13: Add data on planarity/nonplanarity of reconfiguration graph of independent sets under Token Sliding, where the original input graph has $n\in \{6,7,8,9\}$ vertices.