enclosed in parentheses the parent is the vertex you reached just before you reached the destination vertex in this case the parents are all because we've only moved one edge away from if fare is unknown (or meaninglessas from to ait' shown as infinityrepresented by "inf,as in the rail-fare notebook entries notice that the column heads of those vertices that have already been added to the tree are shown in red the entries for these columns won' change minimum distance initiallythe algorithm knows the distances from to other vertices that are exactly one edge from only and are adjacent to aso they're the only ones whose distances are shown the algorithm picks the minimum distance another click on path will show you the message minimum distance from is to vertex the algorithm adds this vertex to the treeso the next click will show you added vertex to tree now is circled in the graphand the column head is in red the edge from to is made darker to show it' also part of the tree column by column in the shortest-path array now the algorithm knowsnot only all the edges from abut the edges from as well so it goes through the shortest-path arraycolumn by columnchecking whether shorter path than that shown can be calculated using this new information vertices that are already in the treehere and bare skipped first column is examined you'll see the message to ca to ( plus edge bc ( less than to (infthe algorithm has found shorter path to than that shown in the array the array shows infinity in the column but from to is (which the algorithm finds in the column in the shortest-path arrayand from to is (which it finds in row column in the adjacency matrixthe sum is the distance is less than infinityso the algorithm updates the shortest-path array for column cinserting this is followed by in parenthesesbecause that' the last vertex before reaching cb is the parent of next the column is examined you'll see the message to da to ( plus edge bd ( greater than or equal to to ( the algorithm is comparing the previously shown distance from to dwhich is (the direct route)with possible route via (that isa- -dbut path - is and edge bd is so the sum is this is bigger than so is not changed