Abstract The NP-complete Vertex Cover problem asks to cover all edges of a graph by small (given) number vertices. It is among the most prominent graph-algorithmic problems. Following recent trend in studying temporal graphs (a sequence graphs, so-called layers, over same vertex set but, time, changing edge sets), we initiate study Multistage . Herein, given graph, goal find for each layer and ...

An important requirement of multiscale spatial databases is that topological consistency is maintained both within individual features and between co-displayed features for all scales at which they may be retrieved. Here we show how a triangulation-based branch-pruning generalisation procedure can be enhanced to enable its output to be used to build topologically-consistent multiscale data stru...

We show that the directed labelled Cayley graphs coincide with the rooted deterministic vertextransitive simple graphs. The Cayley graphs are also the strongly connected deterministic simple graphs of which all vertices have the same cycle language, or just the same elementary cycle language. Under the assumption of the axiom of choice, we characterize the Cayley graphs for all group subsets as...

In this paper we study the robust stability of uncertain quasipolynomials, whose coef£cients may vary in a certain prescribed range. We consider speci£cally the co-called interval and diamond quasipolynomials, and our goal is to develop vertexand edge type-conditions for these quasipolynomial families to be robustly stable independent of delay. Moreover, we also present a number of extensions t...

if $g$ is a connected graph with vertex set $v$, then the eccentric connectivity index of $g$, $xi^c(g)$, is defined as $sum_{vin v(g)}deg(v)ecc(v)$ where $deg(v)$ is the degree of a vertex $v$ and $ecc(v)$ is its eccentricity. in this paper we show some convergence in probability and an asymptotic normality based on this index in random bucket recursive trees.