Diagnosability of star graphs with missing edges

In this paper, we study the system diagnosis on an n-dimensional star under the comparison model. Following the concept of local diagnosability , the strong local diagnosability property is discussed; this property describes the equivalence of the local diagnosability of a node and its degree. We prove that an n-dimensional star has this property, and it keeps this strong property even if there exist n − 3 missing edges in it.