Growth of graph powers

Details Growth of graph powers Growth of graph powers

2010-05-14

arxiv.org/abs/1005.2542v1

Mathematics

Combinatorics

6 pages, 1 figure

Scientific paper

For a graph G, its rth power is constructed by placing an edge between two
vertices if they are within distance r of each other. In this note we study the
amount of edges added to a graph by taking its rth power. In particular we
obtain that either the rth power is complete or "many" new edges are added.
This is an extension of a result obtained by P. Hegarty for cubes of graphs.

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