For a graph G and a set D V (G), define Nr[x] = {xi V (G) : d(x, xi) r} (where d(x, y) is graph theoretic distance) and Dr(x) = Nr[x] D. D is known as an r-identifying code if...
An identifying code of a graph G is a dominating set C such that every vertex x of G is distinguished from all other vertices by the set of vertices in C that are at distance at m...
Let G = (V, E) be a connected undirected graph and S a subset of vertices. If for all vertices v V , the sets Br(v) S are all nonempty and different, where Br(v) denotes the set...
ABSTRACT. Upon the discovery of power laws [8, 16, 30], a large body of work in complex network analysis has focused on developing generative models of graphs which mimick real-wor...
Given a graph G, an identifying code D V (G) is a vertex set such that for any two distinct vertices v1, v2 V (G), the sets N[v1] D and N[v2] D are distinct and nonempty (here...