THE DOMINATION COVER PEBBLING NUMBER FOR SOME CYCLIC GRAPHS AND PATH GRAPHS

The domination cover pebbling number, psi(G), of a graph G, is the smallest number such that some distribution D is an element of P is reachable from every distribution starting with psi(G) (or more) pebbles on G, where P is a set of dominating distributions. In [2], some distributions have not been considered while proving the domination cover pebbling number for complete r-partite graphs and path graphs. And also for the cycle C-6m (m >= 1), reduction of one pebble yields domination covering solution for it. We discuss this here in a detailed manner and also we provide an algorithm to find a domination covering solution for a given distribution of size psi(C-n) on the vertices of C-n. In this paper, we determine the domination cover pebbling number for some cyclic graphs and path graphs using the newly defined psi(G).