nx = 3; ny = 5; G = GridGraph[{nx, ny}];
w = RandomInteger[{1, 6}, EdgeCount[G]];
GG = Graph[EdgeList[G], EdgeWeight -> w, VertexLabels -> "Name",
VertexLabelStyle -> Directive[Blue, Italic, 10],
EdgeLabels -> "EdgeWeight",
EdgeStyle -> Directive[Opacity[0.65`], Blue],
EdgeLabelStyle -> Directive[Black, Italic, 10]] ;
k = FindSpanningTree[GG];
HighlightGraph[GG, k, GraphHighlightStyle -> "Thick"]