1998
DOI: 10.1109/18.661507
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On a new class of codes for identifying vertices in graphs

Abstract: Abstract-We investigate a new class of codes for the optimal covering of vertices in an undirected graph G such that any vertex in G can be uniquely identified by examining the vertices that cover it. We define a ball of radius t centered on a vertex v to be the set of vertices in G that are at distance at most t from v: The vertex v is then said to cover itself and every other vertex in the ball with center v: Our formal problem statement is as follows: Given an undirected graph G and an integer t 1, find a (… Show more

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Cited by 379 publications
(344 citation statements)
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“…One of the interests of these notions lies in their applications to the location of threats in facilities [54,58] and error detection in computer networks [40]. One can also mention applications to routing [44], to bioinformatics [37] (where identifying codes are called differentiating dominating sets) and to measuring the first-order logical complexity of graphs [41] (where locating-dominating sets are calledsieves).…”
Section: Definitions and Problemsmentioning
confidence: 99%
See 1 more Smart Citation
“…One of the interests of these notions lies in their applications to the location of threats in facilities [54,58] and error detection in computer networks [40]. One can also mention applications to routing [44], to bioinformatics [37] (where identifying codes are called differentiating dominating sets) and to measuring the first-order logical complexity of graphs [41] (where locating-dominating sets are calledsieves).…”
Section: Definitions and Problemsmentioning
confidence: 99%
“…The notion that we will mainly study, introduced in 1998 in [40], is the one of an identifying code. Given a graph G and a vertex v of G, we denote by N (v) and by N [v] the open and the closed neighbourhood of v, respectively.…”
Section: Definitions and Problemsmentioning
confidence: 99%
“…the identifying code problem is to find an identifying code of minimum cardinality for any given graph. Identifying codes have been studied extensively since their introduction in 1998 [5], and they have formed a fundamental basis for a wide variety of theoretical work and practical applications.…”
Section: A Identifying Codesmentioning
confidence: 99%
“…Applications such as fault detection and diagnosis in network and specifically in processor arrays [5], location detection in sensor networks [6,7], environmental monitoring in utility networks [10], and others, have been studied extensively, using different approaches that have resulted in a large variety of practical algorithms as well as theoretical results. In this paper we focus on a combinatorial approach, which is closely related to error-correcting codes, and specifically to identifying codes.…”
Section: Introductionmentioning
confidence: 99%
“…Such a subset C ⊆ V satisfying the two requirements is called an identifying code (any nonempty subset of V is called a code). The concept of identifying codes was introduced in [10], where a fault diagnosis was performed in multiprocessor networks.…”
Section: Introductionmentioning
confidence: 99%