Model transformations play a key role in the vision of ModelDriven Engineering. Nevertheless, mechanisms like abstraction, variation and composition for specifying and applying reusable model transformations – like urgently needed for resolving recurring structural heterogeneities – are insufficiently supported so far. Therefore, we propose to specify model transformations by a set of pre-defin...

For a nonempty set S of vertices of a connected graph G, the Steiner distance d(S) of S is the minimum size among all connected subgraphs whose vertex set contains S. For an ordered set W = {Wl, W2,"', Wk} of vertices in a connected graph G and a vertex v of G, the Steiner representation s(vIW) of v with respect to W is the (2k I)-vector where d i1 ,i2, ... ,ij(V) is the Steiner distance d({V,W...

A k-partition Π = {S1,S2, . . . ,Sk} of V (G) is resolving if for every two distinct vertices u and v of a connected graph G, there is a set Si in Π so that the minimum distance between u and a vertex of Si is different from the minimum distance between v and a vertex of Si. A resolving partition Π is said to be connected if each subgraph < Si > induced by Si (1 ≤ i ≤ k) is connected in G. In t...

For an ordered set W = {w1, w2, . . . , wk} of vertices and a vertex v in a connected graph G, the ordered k-vector r(v|W ) := (d(v,w1), d(v,w2), . . . , d(v,wk)) is called the (metric) representation of v with respect to W , where d(x, y) is the distance between the vertices x and y. The set W is called a resolving set for G if distinct vertices of G have distinct representations with respect ...

A resolving set for a graph Γ is a collection of vertices S, chosen so that for each vertex v, the list of distances from v to the members of S uniquely specifies v. The metric dimension μ(Γ) is the smallest size of a resolving set for Γ. We consider the metric dimension of the dual polar graphs, and show that it is at most the rank over R of the incidence matrix of the corresponding polar spac...

We provide upper bounds for the determining number and the metric dimension of tournaments. A set of vertices S ⊆ V (T ) is a determining set for a tournament T if every nontrivial automorphism of T moves at least one vertex of S, while S is a resolving set for T if every two distinct vertices in T have different distances to some vertex in S. We show that the minimum size of a determining set ...

Let G be a (di)graph and S a set of vertices of G. We say S resolves two vertices u and v of G if d(u, S) 6= d(v, S). A partition Π = {P1, P2, . . . , Pk} of V (G) is a resolving partition of G if every two vertices of G are resolved by Pi for some i (1 ≤ i ≤ k). The smallest cardinality of a resolving partition of G, denoted by pd(G), is called the partition dimension of G. A vertex r of G res...

Digital watermarking is a promising technology for protecting intellectual property rights on digital content. Resolving authorship-disputes was one of the first and most propelling applications of robust digital watermarks, and much research effort has gone into protocols for resolving authorship-disputes by means of digital watermarks. Unfortunately, previous proposals lack formal definitions...

For an ordered set W = {w1, w2, . . . , wk} of vertices and a vertex v in a connected graph G, the ordered k-vector r(v|W ) := (d(v, w1), d(v, w2), . . . , d(v, wk)) is called the (metric) representation of v with respect to W , where d(x, y) is the distance between the vertices x and y. The set W is called a resolving set for G if distinct vertices of G have distinct representations with respe...