There are, 1, unlabled trees on, 1, vertices

     The set of Line-Graph cardinalities of depth 3 has, 1, here there are

                                 {[1, 0, 0, 0]}



                 There are, 1, unlabled trees on, 2, vertices

     The set of Line-Graph cardinalities of depth 3 has, 1, here there are

                                 {[2, 1, 0, 0]}



                 There are, 1, unlabled trees on, 3, vertices

     The set of Line-Graph cardinalities of depth 3 has, 1, here there are

                                 {[3, 2, 1, 0]}



                 There are, 2, unlabled trees on, 4, vertices

     The set of Line-Graph cardinalities of depth 3 has, 2, here there are

                          {[4, 3, 2, 1], [4, 3, 3, 3]}



                 There are, 3, unlabled trees on, 5, vertices

     The set of Line-Graph cardinalities of depth 3 has, 3, here there are

                  {[5, 4, 3, 2], [5, 4, 4, 5], [5, 4, 6, 12]}



                 There are, 6, unlabled trees on, 6, vertices

     The set of Line-Graph cardinalities of depth 3 has, 6, here there are

{[6, 5, 4, 3], [6, 5, 5, 6], [6, 5, 5, 7], [6, 5, 6, 10], [6, 5, 7, 15],

    [6, 5, 10, 30]}



                 There are, 11, unlabled trees on, 7, vertices

     The set of Line-Graph cardinalities of depth 3 has, 11, here there are

{[7, 6, 5, 4], [7, 6, 6, 7], [7, 6, 6, 8], [7, 6, 6, 9], [7, 6, 7, 10],

    [7, 6, 7, 12], [7, 6, 8, 16], [7, 6, 8, 18], [7, 6, 9, 21], [7, 6, 11, 34],

    [7, 6, 15, 60]}



                 There are, 23, unlabled trees on, 8, vertices

     The set of Line-Graph cardinalities of depth 3 has, 20, here there are

{[8, 7, 6, 5], [8, 7, 7, 8], [8, 7, 7, 9], [8, 7, 7, 10], [8, 7, 8, 11],

    [8, 7, 8, 12], [8, 7, 8, 13], [8, 7, 8, 14], [8, 7, 9, 17], [8, 7, 9, 19],

    [8, 7, 9, 21], [8, 7, 10, 20], [8, 7, 10, 23], [8, 7, 10, 24],

    [8, 7, 12, 33], [8, 7, 12, 35], [8, 7, 12, 38], [8, 7, 13, 41],

    [8, 7, 16, 65], [8, 7, 21, 105]}



                 Since there are not enough let's tree depth 4

     The set of Line-Graph cardinalities of depth 4 has, 23, here there are

{[8, 7, 6, 5, 4], [8, 7, 7, 8, 12], [8, 7, 7, 9, 17], [8, 7, 7, 9, 18],

    [8, 7, 7, 10, 23], [8, 7, 8, 11, 20], [8, 7, 8, 12, 26], [8, 7, 8, 13, 35],

    [8, 7, 8, 14, 40], [8, 7, 8, 14, 41], [8, 7, 9, 17, 53], [8, 7, 9, 17, 55],

    [8, 7, 9, 19, 70], [8, 7, 9, 21, 84], [8, 7, 10, 20, 65],

    [8, 7, 10, 23, 92], [8, 7, 10, 24, 101], [8, 7, 12, 33, 162],

    [8, 7, 12, 35, 184], [8, 7, 12, 38, 211], [8, 7, 13, 41, 233],

    [8, 7, 16, 65, 470], [8, 7, 21, 105, 945]}

                 There are, 47, unlabled trees on, 9, vertices

     The set of Line-Graph cardinalities of depth 3 has, 37, here there are

{[9, 8, 7, 6], [9, 8, 8, 9], [9, 8, 8, 10], [9, 8, 8, 11], [9, 8, 9, 12],

    [9, 8, 9, 13], [9, 8, 9, 14], [9, 8, 9, 15], [9, 8, 9, 16], [9, 8, 10, 17],

    [9, 8, 10, 18], [9, 8, 10, 19], [9, 8, 10, 20], [9, 8, 10, 22],

    [9, 8, 10, 24], [9, 8, 11, 21], [9, 8, 11, 22], [9, 8, 11, 23],

    [9, 8, 11, 24], [9, 8, 11, 25], [9, 8, 11, 26], [9, 8, 11, 27],

    [9, 8, 12, 28], [9, 8, 12, 30], [9, 8, 13, 30], [9, 8, 13, 36],

    [9, 8, 13, 39], [9, 8, 13, 42], [9, 8, 14, 39], [9, 8, 14, 43],

    [9, 8, 14, 45], [9, 8, 16, 54], [9, 8, 17, 66], [9, 8, 17, 70],

    [9, 8, 18, 73], [9, 8, 22, 111], [9, 8, 28, 168]}



                 Since there are not enough let's tree depth 4

     The set of Line-Graph cardinalities of depth 4 has, 47, here there are

{[9, 8, 7, 6, 5], [9, 8, 8, 9, 13], [9, 8, 8, 10, 18], [9, 8, 8, 10, 19],

    [9, 8, 8, 11, 24], [9, 8, 8, 11, 25], [9, 8, 9, 12, 21], [9, 8, 9, 13, 26],

    [9, 8, 9, 13, 28], [9, 8, 9, 14, 32], [9, 8, 9, 14, 33], [9, 8, 9, 14, 36],

    [9, 8, 9, 15, 42], [9, 8, 9, 15, 43], [9, 8, 9, 16, 48], [9, 8, 10, 17, 45],

    [9, 8, 10, 18, 56], [9, 8, 10, 19, 60], [9, 8, 10, 19, 62],

    [9, 8, 10, 20, 71], [9, 8, 10, 20, 73], [9, 8, 10, 22, 87],

    [9, 8, 10, 24, 102], [9, 8, 11, 21, 64], [9, 8, 11, 22, 71],

    [9, 8, 11, 23, 81], [9, 8, 11, 24, 94], [9, 8, 11, 25, 101],

    [9, 8, 11, 25, 104], [9, 8, 11, 26, 109], [9, 8, 11, 27, 119],

    [9, 8, 12, 28, 113], [9, 8, 12, 30, 136], [9, 8, 13, 30, 111],

    [9, 8, 13, 36, 180], [9, 8, 13, 36, 185], [9, 8, 13, 39, 215],

    [9, 8, 13, 42, 243], [9, 8, 14, 39, 196], [9, 8, 14, 43, 242],

    [9, 8, 14, 45, 265], [9, 8, 16, 54, 336], [9, 8, 17, 66, 475],

    [9, 8, 17, 70, 521], [9, 8, 18, 73, 548], [9, 8, 22, 111, 1020],

    [9, 8, 28, 168, 1848]}

                There are, 106, unlabled trees on, 10, vertices

     The set of Line-Graph cardinalities of depth 3 has, 68, here there are

{[10, 9, 8, 7], [10, 9, 9, 10], [10, 9, 9, 11], [10, 9, 9, 12], [10, 9, 10, 13],

    [10, 9, 10, 14], [10, 9, 10, 15], [10, 9, 10, 16], [10, 9, 10, 17],

    [10, 9, 10, 18], [10, 9, 11, 17], [10, 9, 11, 18], [10, 9, 11, 19],

    [10, 9, 11, 20], [10, 9, 11, 21], [10, 9, 11, 23], [10, 9, 11, 25],

    [10, 9, 12, 22], [10, 9, 12, 23], [10, 9, 12, 24], [10, 9, 12, 25],

    [10, 9, 12, 26], [10, 9, 12, 27], [10, 9, 12, 28], [10, 9, 12, 29],

    [10, 9, 12, 30], [10, 9, 13, 27], [10, 9, 13, 28], [10, 9, 13, 29],

    [10, 9, 13, 30], [10, 9, 13, 31], [10, 9, 13, 32], [10, 9, 13, 33],

    [10, 9, 14, 31], [10, 9, 14, 33], [10, 9, 14, 37], [10, 9, 14, 39],

    [10, 9, 14, 40], [10, 9, 14, 43], [10, 9, 14, 46], [10, 9, 15, 39],

    [10, 9, 15, 40], [10, 9, 15, 41], [10, 9, 15, 42], [10, 9, 15, 43],

    [10, 9, 15, 44], [10, 9, 15, 45], [10, 9, 15, 46], [10, 9, 15, 47],

    [10, 9, 15, 49], [10, 9, 16, 48], [10, 9, 16, 52], [10, 9, 17, 49],

    [10, 9, 17, 57], [10, 9, 17, 58], [10, 9, 18, 67], [10, 9, 18, 71],

    [10, 9, 18, 75], [10, 9, 19, 70], [10, 9, 19, 75], [10, 9, 19, 78],

    [10, 9, 20, 76], [10, 9, 21, 87], [10, 9, 23, 112], [10, 9, 23, 117],

    [10, 9, 24, 120], [10, 9, 29, 175], [10, 9, 36, 252]}



                 Since there are not enough let's tree depth 4

    The set of Line-Graph cardinalities of depth 4 has, 101, here there are

{[10, 9, 8, 7, 6], [10, 9, 9, 10, 14], [10, 9, 9, 11, 19], [10, 9, 9, 11, 20],

    [10, 9, 9, 12, 25], [10, 9, 9, 12, 26], [10, 9, 9, 12, 27],

    [10, 9, 10, 13, 22], [10, 9, 10, 14, 27], [10, 9, 10, 14, 28],

    [10, 9, 10, 14, 29], [10, 9, 10, 15, 32], [10, 9, 10, 15, 33],

    [10, 9, 10, 15, 34], [10, 9, 10, 15, 35], [10, 9, 10, 15, 37],

    [10, 9, 10, 16, 39], [10, 9, 10, 16, 43], [10, 9, 10, 16, 44],

    [10, 9, 10, 16, 45], [10, 9, 10, 17, 50], [10, 9, 10, 18, 56],

    [10, 9, 11, 17, 38], [10, 9, 11, 18, 45], [10, 9, 11, 19, 51],

    [10, 9, 11, 19, 52], [10, 9, 11, 19, 53], [10, 9, 11, 19, 57],

    [10, 9, 11, 20, 62], [10, 9, 11, 20, 64], [10, 9, 11, 21, 67],

    [10, 9, 11, 21, 68], [10, 9, 11, 21, 69], [10, 9, 11, 21, 72],

    [10, 9, 11, 21, 74], [10, 9, 11, 23, 88], [10, 9, 11, 23, 90],

    [10, 9, 11, 25, 105], [10, 9, 12, 22, 65], [10, 9, 12, 23, 70],

    [10, 9, 12, 23, 73], [10, 9, 12, 24, 78], [10, 9, 12, 24, 80],

    [10, 9, 12, 24, 84], [10, 9, 12, 25, 87], [10, 9, 12, 25, 95],

    [10, 9, 12, 26, 98], [10, 9, 12, 26, 103], [10, 9, 12, 26, 105],

    [10, 9, 12, 27, 111], [10, 9, 12, 27, 112], [10, 9, 12, 28, 118],

    [10, 9, 12, 28, 122], [10, 9, 12, 29, 127], [10, 9, 12, 30, 138],

    [10, 9, 13, 27, 90], [10, 9, 13, 28, 104], [10, 9, 13, 29, 115],

    [10, 9, 13, 30, 120], [10, 9, 13, 30, 123], [10, 9, 13, 31, 130],

    [10, 9, 13, 32, 144], [10, 9, 13, 33, 155], [10, 9, 14, 31, 108],

    [10, 9, 14, 33, 127], [10, 9, 14, 37, 183], [10, 9, 14, 37, 186],

    [10, 9, 14, 39, 198], [10, 9, 14, 39, 199], [10, 9, 14, 40, 216],

    [10, 9, 14, 40, 219], [10, 9, 14, 43, 247], [10, 9, 14, 46, 276],

    [10, 9, 15, 39, 174], [10, 9, 15, 40, 194], [10, 9, 15, 41, 202],

    [10, 9, 15, 42, 216], [10, 9, 15, 43, 227], [10, 9, 15, 44, 244],

    [10, 9, 15, 45, 252], [10, 9, 15, 46, 269], [10, 9, 15, 47, 274],

    [10, 9, 15, 49, 298], [10, 9, 16, 48, 264], [10, 9, 16, 52, 320],

    [10, 9, 17, 49, 243], [10, 9, 17, 57, 355], [10, 9, 17, 58, 369],

    [10, 9, 18, 67, 476], [10, 9, 18, 71, 526], [10, 9, 18, 75, 573],

    [10, 9, 19, 70, 488], [10, 9, 19, 75, 558], [10, 9, 19, 78, 600],

    [10, 9, 20, 76, 540], [10, 9, 21, 87, 681], [10, 9, 23, 112, 1026],

    [10, 9, 23, 117, 1096], [10, 9, 24, 120, 1128], [10, 9, 29, 175, 1953],

    [10, 9, 36, 252, 3276]}

                 Since there are not enough let's tree depth 5

    The set of Line-Graph cardinalities of depth 5 has, 106, here there are

{[10, 9, 8, 7, 6, 5], [10, 9, 9, 10, 14, 30], [10, 9, 9, 11, 19, 56],

    [10, 9, 9, 11, 20, 63], [10, 9, 9, 11, 20, 64], [10, 9, 9, 12, 25, 93],

    [10, 9, 9, 12, 26, 101], [10, 9, 9, 12, 27, 108], [10, 9, 10, 13, 22, 55],

    [10, 9, 10, 14, 27, 81], [10, 9, 10, 14, 28, 89], [10, 9, 10, 14, 29, 102],

    [10, 9, 10, 15, 32, 108], [10, 9, 10, 15, 33, 119],

    [10, 9, 10, 15, 34, 128], [10, 9, 10, 15, 35, 140],

    [10, 9, 10, 15, 37, 170], [10, 9, 10, 16, 39, 159],

    [10, 9, 10, 16, 43, 214], [10, 9, 10, 16, 44, 221],

    [10, 9, 10, 16, 44, 225], [10, 9, 10, 16, 45, 233],

    [10, 9, 10, 17, 50, 268], [10, 9, 10, 17, 50, 269],

    [10, 9, 10, 18, 56, 316], [10, 9, 11, 17, 38, 140],

    [10, 9, 11, 18, 45, 196], [10, 9, 11, 19, 51, 236],

    [10, 9, 11, 19, 52, 253], [10, 9, 11, 19, 53, 265],

    [10, 9, 11, 19, 57, 326], [10, 9, 11, 20, 62, 352],

    [10, 9, 11, 20, 64, 381], [10, 9, 11, 21, 67, 389],

    [10, 9, 11, 21, 68, 400], [10, 9, 11, 21, 69, 417],

    [10, 9, 11, 21, 72, 468], [10, 9, 11, 21, 74, 489],

    [10, 9, 11, 23, 88, 632], [10, 9, 11, 23, 90, 652],

    [10, 9, 11, 25, 105, 816], [10, 9, 12, 22, 65, 351],

    [10, 9, 12, 23, 70, 379], [10, 9, 12, 23, 73, 418],

    [10, 9, 12, 24, 78, 450], [10, 9, 12, 24, 80, 484],

    [10, 9, 12, 24, 80, 495], [10, 9, 12, 24, 84, 547],

    [10, 9, 12, 24, 84, 552], [10, 9, 12, 25, 87, 554],

    [10, 9, 12, 25, 95, 693], [10, 9, 12, 26, 98, 691],

    [10, 9, 12, 26, 103, 772], [10, 9, 12, 26, 105, 809],

    [10, 9, 12, 27, 111, 863], [10, 9, 12, 27, 112, 876],

    [10, 9, 12, 28, 118, 934], [10, 9, 12, 28, 122, 1000],

    [10, 9, 12, 29, 127, 1047], [10, 9, 12, 30, 138, 1191],

    [10, 9, 13, 27, 90, 527], [10, 9, 13, 28, 104, 733],

    [10, 9, 13, 29, 115, 868], [10, 9, 13, 30, 120, 899],

    [10, 9, 13, 30, 123, 950], [10, 9, 13, 31, 130, 1025],

    [10, 9, 13, 32, 144, 1231], [10, 9, 13, 33, 155, 1382],

    [10, 9, 14, 31, 108, 651], [10, 9, 14, 33, 127, 871],

    [10, 9, 14, 37, 183, 1743], [10, 9, 14, 37, 186, 1787],

    [10, 9, 14, 39, 198, 1927], [10, 9, 14, 39, 199, 1948],

    [10, 9, 14, 40, 216, 2210], [10, 9, 14, 40, 219, 2249],

    [10, 9, 14, 43, 247, 2663], [10, 9, 14, 46, 276, 3108],

    [10, 9, 15, 39, 174, 1446], [10, 9, 15, 40, 194, 1815],

    [10, 9, 15, 41, 202, 1900], [10, 9, 15, 42, 216, 2139],

    [10, 9, 15, 43, 227, 2295], [10, 9, 15, 44, 244, 2593],

    [10, 9, 15, 45, 252, 2694], [10, 9, 15, 46, 269, 2988],

    [10, 9, 15, 47, 274, 3046], [10, 9, 15, 49, 298, 3440],

    [10, 9, 16, 48, 264, 2792], [10, 9, 16, 52, 320, 3772],

    [10, 9, 17, 49, 243, 2250], [10, 9, 17, 57, 355, 4294],

    [10, 9, 17, 58, 369, 4554], [10, 9, 18, 67, 476, 6435],

    [10, 9, 18, 71, 526, 7375], [10, 9, 18, 75, 573, 8292],

    [10, 9, 19, 70, 488, 6553], [10, 9, 19, 75, 558, 7958],

    [10, 9, 19, 78, 600, 8813], [10, 9, 20, 76, 540, 7548],

    [10, 9, 21, 87, 681, 10380], [10, 9, 23, 112, 1026, 17895],

    [10, 9, 23, 117, 1096, 19570], [10, 9, 24, 120, 1128, 20328],

    [10, 9, 29, 175, 1953, 41748], [10, 9, 36, 252, 3276, 81900]}

                            -----------------------



                        This took, 87094.449, seconds.