Diagnosability of Networks Represented by the Cartesian Product
نویسندگان
چکیده
System level diagnosis that can identify the faulty units in the system was introduced by Preparata, Metze, and Chien [1]. In this area, the fundamental problem is to decide the diagnosability of given networks. We study the diagnosability of networks represented by the cartesian product. Our result is the optimal one with respect to the restriction of degrees of vertices of graphs that represent the networks. key words: system level diagnosis, PMC model, t-diagnosable system, t/t-diagnosable system, cartesian product
منابع مشابه
An approach to conditional diagnosability analysis under the PMC model and its application to torus networks
A general technique is proposed for determining the conditional diagnosability of interconnection networks under the PMC model. Several graph invariants are involved in the approach, such as the length of the shortest cycle, the minimum number of neighbors, γp (resp. γp), over all p-vertex subsets (resp. cycles), and a variant of connectivity, called the r-super-connectivity. An n-dimensional t...
متن کاملThe reliability Wiener number of cartesian product graphs
Reliability Wiener number is a modification of the original Wiener number in which probabilities are assigned to edges yielding a natural model in which there are some (or all) bonds in the molecule that are not static. Various probabilities naturally allow modelling different types of chemical bonds because chemical bonds are of different types and it is well-known that under certain condition...
متن کاملThe Nature Diagnosability of Bubble - sort Star Graphs under the PMC Model and MM * Model
55 www.ijeas.org 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 fault set can contain all the neighbors of any fault-free vertex in the system, which is called the nature diagnosability of ...
متن کاملThe Merrifield-Simmons indices and Hosoya indices of some classes of cartesian graph product
The Merrifield-Simmons index of a graph is defined as the total number of the independent sets of the graph and the Hosoya index of a graph is defined as the total number of the matchings of the graph. In this paper, we give formula for Merrifield-Simmons and Hosoya indices of some classes of cartesian product of two graphs K{_2}×H, where H is a path graph P{_n}, cyclic graph C{_n}, or star gra...
متن کاملSharp Upper bounds for Multiplicative Version of Degree Distance and Multiplicative Version of Gutman Index of Some Products of Graphs
In $1994,$ degree distance of a graph was introduced by Dobrynin, Kochetova and Gutman. And Gutman proposed the Gutman index of a graph in $1994.$ In this paper, we introduce the concepts of multiplicative version of degree distance and the multiplicative version of Gutman index of a graph. We find the sharp upper bound for the multiplicative version of degree distance and multiplicative ver...
متن کامل