Abstract In this paper, we use a robust lower directional derivative and provide some sufficient conditions to ensure the strong regularity of given mapping at certain point. Then, discuss Hoffman estimation achieve results for estimate distance set solutions system linear equalities . The advantage our is that it allows one calculate coefficient error bound.

Strongly regular graphs form an important class of graphs which lie somewhere between the highly structured and the apparently random. This chapter gives an introduction to these graphs with pointers to more detailed surveys of particular topics.

In this paper, we show that the minimum number of vertices whose removal disconnects a connected strongly regular graph into non-singleton components, equals the size of the neighborhood of an edge for many graphs. These include blocks graphs of Steiner 2-designs, many Latin square graphs and strongly regular graphs whose intersection parameters are at most a quarter of their valency.