Cycle Properties of s -vertex Connected Graphs

摘要

The cycle properties of s -vertex connected graph are studied as follows pancyclicity and fully cycle extensibility. Two conclusions are drawn by way of argument: Let G be a s-vertex connected graph, if s≤ (|G|+1)/2, then G is fully cycle extendable. Here the upper bound (n+1)/2 of s is best possible. Let G be a s-vertex connected graph, if s≤ (|G|+1)/2, then G is a pancyclic graph or G≈K_((s-1), (s-2)).