The minimum identifying code graphs
Discrete Applied Mathematics
On a new class of codes for identifying vertices in graphs
IEEE Transactions on Information Theory
Watching systems in graphs: An extension of identifying codes
Discrete Applied Mathematics
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Let G be a graph, u be a vertex of G, and B(u)(or B"G(u)) be the set of u with all its neighbors in G. A set S of vertices is called an identifying set of G if there exists a function f from V(G) to the set of all nonempty subsets of S such that (i) for each vertex u in G, f(u)@?B(u), and (ii) for every pair of distinct vertices u and v, f(u) and f(v) are distinct. f is called a choice identification of G with respect to S. The choice identification number@i"c(G) is the cardinality of a minimum identifying set of G. In this paper, we study the identifying sets in graphs, give a polynomial-time algorithm to find a minimum identifying set of a tree, and determine the choice identification numbers of complete bipartite graphs.