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] : True ↔ ∀ (G : SimpleGraph α) [inst : DecidableRel G.Adj], G.Connected → have C := G.graphCenter; have M := {v : α | G.degree v = G.maxDegree}; ⌈G.distavg C + G.distavg M⌉ ≤ ↑G.path

WOWII Conjecture 34

For a simple connected graph G, path(G) ≥ ⌈dist_avg(C, V) + dist_avg(M, V)⌉, where path(G) is the floor of the average distance of G, C is the set of center vertices (those with minimum eccentricity), M is the set of maximum-degree vertices, and dist_avg(S, V) is the average distance from all vertices to the set S.