A path in a graph  is an uphill path if  for every A subset  is an uphill dominating set “UDS” if every vertex  lies on an uphill path originating from some vertex in S. The uphill domination number of G is denoted by 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  for Mycielski’s graph.

uphill path, uphill domination number, Mycielski’s graph.