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The staggered model is the set of quantum walks based on the notion of graph tessellation , which is a new concept in graph theory . The evolution operator of a staggered quantum walk is obtained from a graph tessellation cover . A graph tessellation is a partition of the vertex set into cliques , and a graph tessellation cover is a set of tessellations whose union covers the edge set. A clique is a subset of the vertex set that induces a complete subgraph. Two vertices in a clique are neighbors, and the cliques of a tessellation specify which vertices are reachable after one step once given the location of the walker.