Identifying and locating-dominating codes on chains and cycles
European Journal of Combinatorics
European Journal of Combinatorics
On graphs on n vertices having an identifying code of cardinality ⌈log2(n + 1)⇸
Discrete Applied Mathematics
Note: On the size of identifying codes in binary hypercubes
Journal of Combinatorial Theory Series A
A linear algorithm for minimum 1-identifying codes in oriented trees
Discrete Applied Mathematics
Minimal identifying codes in trees and planar graphs with large girth
European Journal of Combinatorics
Extremal graphs for the identifying code problem
European Journal of Combinatorics
On a new class of codes for identifying vertices in graphs
IEEE Transactions on Information Theory
Two families of optimal identifying codes in binary Hamming spaces
IEEE Transactions on Information Theory
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In an undirected graph G, a subset C@?V(G) such that C is a dominating set of G, and each vertex in V(G) is dominated by a distinct subset of vertices from C, is called an identifying code of G. The concept of identifying codes was introduced by Karpovsky, Chakrabarty and Levitin in 1998. For a given identifiable graph G, let @c^I^D(G) be the minimum cardinality of an identifying code in G. In this paper, we show that for any connected identifiable triangle-free graph G on n vertices having maximum degree @D=3, @c^I^D(G)@?n-n@D+o(@D). This bound is asymptotically tight up to constants due to various classes of graphs including (@D-1)-ary trees, which are known to have their minimum identifying code of size n-n@D-1+o(1). We also provide improved bounds for restricted subfamilies of triangle-free graphs, and conjecture that there exists some constant c such that the bound @c^I^D(G)@?n-n@D+c holds for any nontrivial connected identifiable graph G.