New Classes of Graceful Trees

<div>Graceful labeling of an extended super-caterpillar with root at vertex <svg height="6.25996pt" id="M142" style="vertical-align:-0.2130003pt" version="1.1" viewbox="-0.0498162 -6.04696 6.23276 6.25996" width="6.23276pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.0136,0,0,-0.0136,0,0)"><path d="M219 86C216 168 211 250 206 337C201 410 189 448 163 448C131 448 79 396 43 344L60 322C91 359 110 375 118 375S132 358 136 298C141 238 152 81 155 -12H182C242 62 331 177 390 258C435 321 451 360 451 391C450 424 432 448 408 448C390 448 372 435 366 419C362 410 362 401 366 394C373 383 376 367 376 350C376 283 262 138 221 86H219Z" id="g185-40"></path><glyph.data ascent="989" descent="-303" horiz-adv-x="447" vert-adv-y="447"></glyph.data></g></svg>.</div>

Journal of Discrete Mathematics

New Classes of Graceful Trees

Figure 9