Draw a graph that models the connecting relationships in the floorplan below. The vertices represent the rooms and the edges represent doorways connecting the rooms. Vertex F\displaystyle {F} represents the outdoors.
[Graphs generated by this script: initPicture(0,250,0,210);line([10,190],[65,190]);line([65,185],[65,195]);line([75,185],[75,195]);line([75,190],[125,190]);line([125,190],[240,190]);line([10,190],[10,100]);line([125,190],[125,100]);line([240,190],[240,100]);line([10,100],[44,100]);line([44,95],[44,105]);line([54,95],[54,105]);line([54,100],[83,100]);line([83,100],[125,100]);line([125,100],[139,100]);line([139,95],[139,105]);line([149,95],[149,105]);line([149,100],[167,100]);line([167,100],[201,100]);line([201,95],[201,105]);line([211,95],[211,105]);line([211,100],[240,100]);line([10,10],[44,10]);line([44,15],[44,5]);line([54,15],[54,5]);line([54,10],[83,10]);line([83,10],[101,10]);line([101,5],[101,15]);line([111,5],[111,15]);line([111,10],[125,10]);line([125,10],[139,10]);line([139,5],[139,15]);line([149,5],[149,15]);line([149,10],[167,10]);line([167,10],[240,10]);line([10,10],[10,52]);line([5,52],[15,52]);line([5,62],[15,62]);line([10,62],[10,100]);line([83,10],[83,52]);line([78,52],[88,52]);line([78,62],[88,62]);line([83,62],[83,100]);line([167,10],[167,52]);line([162,52],[172,52]);line([162,62],[172,62]);line([167,62],[167,100]);line([240,10],[240,52]);line([235,52],[245,52]);line([235,62],[245,62]);line([240,62],[240,100]);text([67,145],'A');text([182,145],'B');text([45,50],'C');text([122,50],'D');text([200,50],'E');text([130,200],'F');]
Is it possible to find a path through the house that uses each doorway once? If so, enter the sequence of rooms(vertices) visited, for example ABDEA. If it is not possible, enter DNE.



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