The Almost Uniquely Pancyclic Graphs Of Outplannar Graphs

Let G be a simple Hamilton graph with n vertices. If there exists m(3≤mkⁱ and Γ_kⁱ .We further discuss the almost uniquely pancyclic graphs in these two kinds of graphs and then obtain the following results:1) If and only if (m,n) e {(3,4), (4,6), (5,9), (7,9), (8,9), (5,14)},there are (m,n) - AUP graphs in Γ_k^k-1 .(2) Let G ∈ Γ_k³(k≥ 5), then G is not almost uniquely pancyclic graph.(3) Let G ∈Γ_k³(k≥ 5), then G is not almost uniquely pancyclic graph. and propose two conjectures:(1)There is no almost uniquely pancyclic graph in Γ_kⁱ(i≥ 4). (2)There is no almost uniquely pancyclic graph in Γ_kⁱ(i≥ 4).