MINIMUM CONVEX COVER OF SPECIAL NONORIENTED GRAPHS

Radu BUZATU State University of Moldova

Аннотация

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 covered 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. Keywords: nonoriented graphs, convex covers, convex number, operations, join, cartesian product, lexicographic product, corona.