Written on the Wall II - Conjecture 34 #
Reference: E. DeLaVina, Written on the Wall II, Conjectures of Graffiti.pc
theorem
WrittenOnTheWallII.GraphConjecture34.conjecture34
{α : Type u_1}
[Fintype α]
[DecidableEq α]
[Nontrivial α]
(G : SimpleGraph α)
(h_conn : G.Connected)
:
WOWII Conjecture 34
Let path(G) be the floor of the average distance of a connected graph G.
Then
path(G) ≥ ceil( distavg(G, center) + distavg(G, maxEccentricityVertices G) ).