The G-conditional Diagnosability Of (n,k)-Star Graph Under PMC And MM* Model

With the rapid development of cloud computing,large-scale parallel computer system is widely used.However,the increase in the number of parallel processors in large-scale computer systems also poses a problem that the failure rate of system components is significantly enhanced.When confronted with this situation,the faulty processors in the system can be identified through a specific process such as system fault diagnosis.The diagnosability is the maximum of fault processors those can be identified though a diagnosis,which plays an important role in measuring its reliability.Since traditional diagnosability underestimates the ability of large-scale internetwork to self-diagnose,Lai et al strained the neighborhood of nodes in large-scale computer systems,that and proposed conditional diagnosability,which restricted every vertex contains at least one healthy neighbor.Afterwards,Peng et al.required that each non-faulty vertex should have at least g non-faulty neighbours,and the g-good neighbor diagnosability was brought forward.Inspired by the concept of conditional diagnosability and the g-good-neighbor conditional diagnosability,we require that each node in the system has at least g non-faulty vertices,and thus put forward g-theconditional diagnosability.In this paper,we investigate the g-conditional diagnosability of（n,k）-star graphs under the PMC model.We show the g-conditional diagnosability of（n,2）-star graphs under the PMC model is t_g(S_n,2)=n+g-1for n≥5 1≤g≤（n-3）/2;and the 2-conditional diagnosability of（n,k）-star graphs under the PMC model ist₂(S_n,k)=n+5k-9 for n≥4,3≤k≤n-1.We also investigate the g-conditional diagnosability of（n,k）-star graphs under the MM*model.We show the g-conditional diagnosability of（n,k）-star graphs under the MM*model ist_g(S_n,2)=n+g-1 for n≥7,2≤g≤（n-）3/2 and the 1-conditional diagnosability of（n,k）-star graphs under the MM*model is t₁(S_n,2)=n-1 for n≥4.Finally,we show the 2-conditional diagnosability of（n,k）-star graphs under MM*model is t₂(S_n,k)=n+5k-9 for n≥4,3≤k≤n-1.