Let G=(V, E) be a simple connected graph
of order
[mid ]V[mid ]=n[ges ]2 and minimum degree
δ, and let 2[les ]s[les ]n. We define two parameters,
the s-average distance μs(G) and
the
s-average nearest neighbour distance
Λs(G), with respect to each of which
V contains an
extremal subset X of order s with vertices
‘as spread out as possible’ in G. We compute
the exact values of both parameters when G is the cycle
Cn, and show how to obtain
the corresponding optimal arrangements of X. Sharp upper and lower
bounds are then
established for Λs(G), as functions
of
s, n and δ, and the extremal graphs described.