Edge Growth in Graph Cubes
classification
🧮 math.CO
cs.DM
keywords
graphaveragebestboundciteconnectedcubesdegree
read the original abstract
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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