Devoted to the study on the theory of H-connected space,which has been investigated by Jungck [1] in detail,we first give Jungck’s theorem another proof free from Whyburn [2] ,and then give another theorem in which“compact”hypothesis in Jungck’s theorem is replaced by the locally connected one.

It is proved that if G is conected, locally connected graph on at least three vertices such that the set of claw centers is independent, and if the subgraph induced by the neighbor of v is strong 2-dominated for any claw centre v , then G is fully cycle extendable.

In this paper, we prove that if G is connected, locally connected graph on at least three vertices such that the set of claw centres B is independent, and if G-B is locally connected, then G is fully cycle extendable.

This paper first presents two different mechanisms maintaining local connectivity AODV routing protocol:LL mechanism based on link layer feedback information and Hello mechanism of network layer,and compares the performance of AODV routing protocol under these two mechanisms through NS2.

In this paper, based on the theory of connectivity of filled Julia Setsfor even quartic polynomials, and local connectivity of Julia sets, connectivity offilled Julia sets for a class of quartic polynomials are concerned.