Abstract:

         A graph G is a ［s,t］-graph if there are at least t edges in every included subgraph of s vertices. Let H be a graph. A graph G is H-locally connected if G［N（F）-V（F）］ is connected for its any subgraph F isomorphic to H. This paper proves that a connected and P₃ locally connected ［5,3］-graph,whose order n≥8 ,is 1-2 extendable. (P₃ is an order 3 path.)

Key words: ［s,t］-graph, H-locally connected graph, 1-2 extendable graph