Ordering Acyclic Connected Structures of Trees Having Greatest Degree-Based Invariants

<div>Acyclic connected graphs <svg height="9.25986pt" id="M117" style="vertical-align:-0.2455397pt" version="1.1" viewbox="-0.0498162 -9.01432 12.0001 9.25986" width="12.0001pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M896 675C863 652 826 634 783 634C683 634 549 687 439 687C259 687 128 601 128 473C128 383 196 329 279 329C392 329 469 405 496 541H476C440 428 385 359 286 359C224 359 169 400 169 480C169 566 257 641 382 641C475 641 622 584 731 584C796 584 862 620 907 657L896 675ZM658 553C579 484 521 424 454 277C364 81 295 16 184 16C120 16 82 44 78 79H80C87 68 100 67 108 67C136 67 153 89 153 116S131 165 104 165C69 165 43 139 43 91C43 31 110 -15 191 -15C263 -15 321 6 378 45C463 101 526 197 557 304C588 413 618 487 671 539L658 553Z"></path></g></svg> having greatest <span class="nowrap"><svg height="11.8174pt" id="M118" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -8.6359 17.3119 11.8174" width="17.3119pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M962 650H795L470 145L347 650H176L170 622C268 613 275 606 244 503L190 322C150 188 132 126 118 91C102 50 80 33 18 28L12 0H245L251 28C175 35 170 48 174 93C177 128 191 180 220 284L292 542H294C331 392 383 150 409 4H432L774 555H776L714 137C700 40 694 34 612 28L606 0H868L874 28C793 34 784 37 797 137L849 533C859 612 863 616 956 622L962 650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,12.22,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"></path></g></svg>.</span></div>

Complexity

fig5

Figure 5

Figure 5: Ordering Acyclic Connected Structures of Trees Having Greatest Degree-Based Invariants 