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For a graph G, its rth power G^r has the same vertex set as G, and has an edge between any two vertices within distance r of each other in G. We give a lower bound for the number of edges in the rth p...
The kth power of a simple graph G, denoted Gk, is the graph with vertex set V (G)where two vertices are adjacent if they are within distance k in G. We are interested in nding lower bounds on the ave...