Some remarks on operations on graphs

Abstract

In this paper we investigate the closedness of some known operations on certain kinds of graphs. We show that the operations, Cartesian product and Tensor product are closed on Hamiltonian, Eulerian, and perfect graphs while they are not closed on triangulated graphs, it also the operation, join product, is shown to be not closed on Eulerian graphs but is closed on Hamiltonian, perfect and triangulated graphs. Other operations and graphs are also investigated.