Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In graph theory, a branch of mathematics, the simplex graph (G) of an undirected graph G is itself a graph, with one node for each clique (a set of mutually adjacent vertices) in G. Two nodes of (G) are linked by an edge whenever the corresponding two cliques differ in the presence or absence of a single vertex. The empty set is included as one of the cliques of G that are used to form the clique graph, as is every set of one vertex and every set of two adjacent vertices. Therefore, the simplex graph contains within it a subdivision of G itself. The simplex graph of a complete graph is a hypercube graph, and the simplex graph of a cycle graph of length four or more is a gear graph. The simplex graph of the complement graph of a path graph is a Fibonacci cube.

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