Manipulate[GraphicsRow[{HighlightGraph[g3,{1,stepedge3[[;;i]]},GraphStyle->"BasicBlue",GraphHighlightStyle->"Thick"],HighlightGraph[tree3,{1,stepedge3[[;;i]]},GraphStyle->"BasicBlue",GraphHighlightStyle->"Thick"]},ImageSize->500],{{i,0,"step"},0,15,1},Initialization:>(g3=PetersenGraph[8,1];{pred3,edges3}=Reap[BreadthFirstScan[g3,1,{"FrontierEdge"->Sow}]];
tree3=TreeGraph[edges3[[1]]];stepedge3=edges3[[1]])]