The Winimum Degree of a Critically n-Line-Connected Graph

Abstract:

      A graph G is said to be Critically n-line-connected if it is n-line-connected. but for each x∈G, λ (G - x )≤n- 1 .The following result is proved; Every critically n-line-connected graph contains at least two vertices of degree n, and then this lower bound is best possible as n≥ 3 .