Graphs where every k-subset of vertices is an identifying set - Archive ouverte HAL
Article Dans Une Revue Discrete Mathematics and Theoretical Computer Science Année : 2014

Graphs where every k-subset of vertices is an identifying set

Résumé

Let $G=(V,E)$ be an undirected graph without loops and multiple edges. A subset $C\subseteq V$ is called \emph{identifying} if for every vertex $x\in V$ the intersection of $C$ and the closed neighbourhood of $x$ is nonempty, and these intersections are different for different vertices $x$. Let $k$ be a positive integer. We will consider graphs where \emph{every} $k$-subset is identifying. We prove that for every $k>1$ the maximal order of such a graph is at most $2k-2.$ Constructions attaining the maximal order are given for infinitely many values of $k.$ The corresponding problem of $k$-subsets identifying any at most $\ell$ vertices is considered as well.
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Dates et versions

hal-00362184 , version 1 (22-07-2015)

Identifiants

Citer

Sylvain Gravier, Svante Janson, Tero Laihonen, Sanna Ranto. Graphs where every k-subset of vertices is an identifying set. Discrete Mathematics and Theoretical Computer Science, 2014, Vol. 16 no. 1 (1), pp.73-88. ⟨10.46298/dmtcs.1253⟩. ⟨hal-00362184⟩
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