Edge Growth in Graph Cubes

Details Edge Growth in Graph Cubes Edge Growth in Graph Cubes

2010-09-02

arxiv.org/abs/1009.0343v1

Mathematics

Combinatorics

Scientific paper

We show that for every connected graph $G$ of diameter $\ge 3$, the graph
$G^3$ has average degree $\ge 7/4 \delta(G)$. We also provide an example
showing that this bound is best possible. This resolves a question of Hegarty
\cite{PH}.

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