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Edge growth in graph powers
Edge growth graph powers
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2012/2/29
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...
Edge Growth in Graph Cubes
Edge Growth Graph Cubes
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2010/11/29
We show that for every connected graph G of diameter 3, the graph G3 has average degree 7
4(G). We also provide an example showing that this bound is best possible. This resolves a question of H...