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<https://discovery.ucl.ac.uk/id/eprint/10112671> <http://purl.org/dc/terms/title> "Edge growth in graph powers"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10112671> <http://purl.org/ontology/bibo/abstract> "For a graph G, its rth power G is defined as the graph with the same vertex set as G, and an edge between any two vertices whenever they are within distance r of each other in G. Motivated by a result from additive number theory, Hegarty raised the question of how many new edges G has when G is a regular, connected graph with diameter at least r. We address this question for r ≠ 3, 6. We give a lower bound for the number of edges in the rth power of G in terms of the order of G and the minimal degree of G. As a corollary, for r ≠3, 6, we determine how small the ratio e(G )/e(G) can be for regular, connected graphs of diameter at least r. r r r"^^<http://www.w3.org/2001/XMLSchema#string> .
<https://discovery.ucl.ac.uk/id/eprint/10112671> <http://purl.org/dc/terms/date> "2014-01-14" .
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