Magnetic separation in graphs

Vertex and edge operations are very popular tools in studying several properties of graphs, as they help us to calculate complex statements by means of easier or well-known ones. Deletion is probably the most important graph operation. If the vertex to be deleted is a cut vertex, the situation is much simpler as the number of components is increased and the remaining components are easier to deal with. The classical vertex removal operation is studied in relation to several topological graph indices, independence number, chromatic number and many other graph parameters. Here, similar methods are applied to study the magnetic separation and vertex separation of graphs.In this paper, motivated by the usefulness of this deletion operation, we introduce two more novel vertex removal operations, named as magnetic separation and vertex separation and study the effect of these three operations for several indices and graphs.