On the covering of vertices for fault diagnosis in hypercubes☆
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Cited by (21)
New results of identifying codes in product graphs
2021, Applied Mathematics and ComputationCitation Excerpt :In this paper, novel upper bounds are presented for the identifying code of four classes of graph operations. The identifying code for some classes of graphs had been studied by many scientists (see for example, paths [2], cycles [2,13,25], hypercubes [3,15,18,21] and infinite grids [1,6,14]). Also, the identifying codes of some product graphs have been investigated, e.g., direct product graphs [23], lexicographic product graphs [9], corona product graphs [8], Cartesian product graphs [19,20] and Cartesian product of two cliques [12].
Identifying codes of corona product graphs
2014, Discrete Applied MathematicsIdentifying codes of the direct product of two cliques
2014, European Journal of CombinatoricsCitation Excerpt :In this regard various families of graphs have been studied, including trees [3], paths [2,5,15], cycles [2,9,21,5,15], and infinite grids [1,6,12]. In terms of graph products, a few of the more recent results have been in the study of hypercubes [4,13,14,17,20], the Cartesian product of cliques [10,8], and the lexicographic product of two graphs [7]. A natural problem (posed by Klavžar [18] at the Bordeaux Workshop on Identifying Codes in 2011) is to determine the order of a minimum identifying code in the direct product of two complete graphs.
Ratewise-optimal non-sequential search strategies under constraints on the tests
2008, Discrete Applied MathematicsCitation Excerpt :This is then improved in (iii) of Theorem 1 to a worst case constraint using a familiar large deviation argument. Finally, in Section 6 we settle a separation problem with balls in Hamming space, which originated in the theory of diagnosis [8]. Here we interpret the problem as a covering problem and achieve the goal with the Covering Lemma of [2], whereas the previous method used on the first problem fails and vice versa!
Monotonicity of the minimum cardinality of an identifying code in the hypercube
2006, Discrete Applied MathematicsOn the density of identifying codes in the square lattice
2002, Journal of Combinatorial Theory. Series B
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This research was supported in part by the National Science Foundation under grant no. MIP 9630096, and by NATO under grant no. 910411.