Graphs which Locally Mirror the Hypercube Structure
Jack Koolen1999, Information Processing Letters
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Abstract
Let Qn be the n-cube and let Qnk be the subgraph of Qn induced by the vertices at distance ≤k from a given vertex. Qnk-like graphs are introduced as graphs in which for any vertex u the set of vertices at distance ≤k from u induces a Qnk. Two characterizations of Qnk-like graphs are given and an O(d|V(G)|2) recognition algorithm is presented, where d is the degree of a given d-regular graph G. Several examples of Qnk-like graphs are also listed.
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