Codes Identifying Sets of Vertices
AAECC-14 Proceedings of the 14th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Minimizing the size of an identifying or locating-dominating code in a graph is NP-hard
Theoretical Computer Science
On a new class of codes for identifying vertices in graphs
IEEE Transactions on Information Theory
Robust location detection with sensor networks
IEEE Journal on Selected Areas in Communications
Joint Monitoring and Routing in Wireless Sensor Networks Using Robust Identifying Codes
Mobile Networks and Applications
The minimum identifying code graphs
Discrete Applied Mathematics
On the size of identifying codes in triangle-free graphs
Discrete Applied Mathematics
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Identifying codes were defined to model fault diagnosis in multiprocessor systems. They are also used for the design of indoor detection systems based on wireless sensor networks. When designing such systems, one is usually interested in finding a network structure which minimizes the cardinality of such a code. Given a graph G on n vertices, it is easy to see that the minimum cardinality of an identifying code of G is at least ⌈log2(n + 1)⌉. In this paper, we provide a construction of all the optimal graphs for the identification of vertices, that is to say graphs on n vertices having an identifying code of cardinality ⌈log2(n + 1)⌉. We also compute various parameters of these graphs.