Distances in Graphs

Details Distances in Graphs Distances in Graphs

2010-11-10

arxiv.org/abs/1011.2450v1

Mathematics

Combinatorics

12 pages, 1 figure

Scientific paper

We suggest a new type of problem about distances in graphs and make several
conjectures. As a first step towards proving them, we show that for
sufficiently large values of $n$ and $k$, a graph on $n$ vertices that has no
three vertices at pairwise distance $k$ has at most $\frac{(n-k+1)^2}{4}$ pairs
of vertices at distance $k$.

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