A Note on the Nature Diagnosability of Alternating Group Graphs Under the PMC Model and MM* Model

Abstract

Many multiprocessor systems have interconnection networks as underlying topologies and an interconnection network is usually represented by a graph where nodes represent processors and links represent communication links between processors. No faulty set can contain all the neighbors of any fault-free node in the system, which is called the nature diagnosability of the system. Diagnosability of a multiprocessor system is one important study topic. As a favorable topology structure of interconnection networks, the n-dimensional alternating group graph AGn has many good properties. In this paper, we prove the following. (1) The nature diagnosability of AGn is 4n − 10 for n − 5 under the PMC model and MM* model. (2) The nature diagnosability of the 4-dimensional alternating group graph AG4 under the PMC model is 5. (3) The nature diagnosability of AG4 under the MM* model is 4.