A vertex set S of a graph G is convex if all vertices of every shortest path between two of its vertices are in S. We say that G has a convex p-cover if X (G)can be overed by p convex sets. The convex cover number of G Is the least p 2 for which G has a convex p-cover.In particular, the nontrivial convex cover number of G is the least p 2 for which G has a convex p-cover, where every set contains at least 3 elements.
In this paper we determine convex cover number and nontrivial convex cover number of special graphs resulting from some operations.
We examine graphs resulting from join of graphs, Cartesian product
of graphs, lexicographic product of graphs and corona of graphs.
A stochastic algorithm is proposed and analyzed, that is a probabilistic generalization of gradient method, for solving convex models. A random change of „old” partial derivatives with „new” ones is performed from one ...
Buzatu, Radu(Institutul de Matematică şi Informatică al AŞM, 2021)
Let G be a connected graph. We say that a set S ⊆ X(G) is convex in G
if, for any two vertices x, y ∈ S, all vertices of every shortest path between x and y are
in S. If 3 ≤ |S| ≤ |X(G)| − 1, then S is a nontrivial set. ...
Buzatu, Radu; Cataranciuc, Sergiu(Academy of Sciences of Moldova, 2015)
We study some properties of minimum convex covers and minimum convex partitions of simple graphs. We establish existence of graphs with fixed number of minimum convex covers and minimum convex partitions. It is known that ...
