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

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

2009-02-03

arxiv.org/abs/0902.0443v1

Mathematics

Combinatorics

21 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Graphs where every k-subset of vertices is an identifying set does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Graphs where every k-subset of vertices is an identifying set, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Graphs where every k-subset of vertices is an identifying set will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-297008