Abstract
A path P = [v(1), v(2), ..., v(k)] in a graph G = (V, E) is an uphill path if (v(i))deg <= deg(v(i+1)) for every 1 <= i <= k. A subset S subset of V (G) is an uphill dominating set "UDS" if every vertex v(i) is an element of V (G) lies on an uphill path originating from some vertex in S. The uphill domination number of G is denoted by gamma(up)(G)g and is the minimum cardinality of the UDSs of G. In this paper, we establish the uphill domination number of some families of standard graphs, and obtain some properties of an uphill domination number of graph operations. Also, an upper bound of the uphill domination number for the tensor product of two graphs is found. In addition, we study gamma(up)(G)g for Mycielski's graph.