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 graphs on n vertices having an identifying code of cardinality ⌈log2(n + 1)⇸
Discrete Applied Mathematics
On a new class of codes for identifying vertices in graphs
IEEE Transactions on Information Theory
Choice identification of a graph
Discrete Applied Mathematics
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Let G be a graph and B(u) be the set of u with all of its neighbors in G. A set S of vertices is called an identifying code of G if, for every pair of distinct vertices u and v, both B(u)@?S and B(v)@?S are nonempty and distinct. A minimum identifying code of a graph G is an identifying code of G with minimum cardinality and M(G) is the cardinality of a minimum identifying code for G. A minimum identifying code graph G of order n is a graph with M(G)=@?log"2(n+1)@? having the minimum number of edges. Moncel (2006) [5] constructed minimum identifying code graphs of order 2^m-1 for m=2 and left the same problem but for arbitrary order open. In this paper, we aimed at the construction of connected minimum identifying code graphs in order to solve this problem for integer order greater than or equal to 4. Furthermore, we discussed some related properties.