Sharp Bounds on the Spectral Radii of Uniform Hypergraphs concerning Diameter or Clique Number

<div>3-uniform <span class="nowrap"><svg height="13.365pt" id="M265" style="vertical-align:-4.350679pt" version="1.1" viewbox="-0.0498162 -9.01432 32.1718 13.365" width="32.1718pt" 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="M46 650V622C120 617 128 613 128 525V125C128 42 120 34 40 28V0H311V28C221 34 212 39 212 124V281L286 262C297 261 316 261 331 263C429 275 526 338 526 468C526 533 501 579 462 609C422 638 364 650 293 650H46ZM212 559C212 588 215 600 223 606C230 613 251 618 279 618C361 618 430 572 430 464C430 337 350 302 285 302C252 302 225 309 212 314V559Z"></path></g><g transform="matrix(.013,0,0,-0.013,7.319,0)"><path d="M771 669C722 624 660 598 616 598C593 598 565 610 530 629C460 664 429 678 388 678C284 678 211 602 211 527C211 453 270 401 350 401C418 401 468 443 501 508L483 517C450 464 405 431 352 431C288 431 252 473 252 525S306 626 370 626C398 626 435 612 472 592C525 563 556 548 596 548C607 548 623 550 632 553L633 550C510 448 474 360 391 210C314 77 264 16 181 16C121 16 79 48 75 79H77C84 68 97 66 106 66C134 66 150 90 150 115C150 144 130 165 103 165C63 165 40 130 40 91C40 38 96 -15 183 -15C301 -15 418 42 546 321C553 310 560 306 580 306C619 306 620 284 620 275C620 211 535 149 535 70C535 21 581 -12 628 -12C689 -12 755 40 830 132L811 147C736 61 680 18 642 18C621 18 610 29 610 52C610 93 686 163 686 232C686 263 673 286 638 321V323C721 350 782 402 849 522C876 570 898 630 916 646H917C918 613 943 601 962 601C990 601 1004 621 1004 646C1004 674 981 687 953 687C900 687 834 608 741 471C684 385 650 354 609 346C596 358 582 360 567 360C627 465 677 573 784 653L771 669Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,20.436,3.132)"><path d="M290 377C321 398 342 415 358 430C378 450 389 473 389 502C389 578 329 635 238 635H237C184 635 137 610 109 578L64 515L88 493C112 529 154 573 208 573S303 542 303 482C303 409 233 370 141 341L149 308C165 313 190 319 215 319C272 319 341 283 341 193C342 98 292 43 222 43C163 43 122 72 96 94C88 101 79 100 70 94C61 87 47 73 46 60C44 47 48 37 62 23C76 10 118 -12 165 -12C238 -12 430 62 430 223C430 297 379 359 290 375V377Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,24.868,3.132)"><path d="M98 134C72 134 46 117 46 90C46 73 55 65 60 64C95 55 124 32 124 -4C124 -42 95 -68 44 -89L57 -123C122 -104 194 -60 194 22C194 94 136 134 98 134Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,27.025,3.132)"><path d="M462 177V227H365V632H320C217 496 116 350 21 208V177H284V109C284 43 280 38 190 31V0H451V31C369 38 365 43 365 108V177H462ZM284 227H88C155 336 218 430 282 519H284V227Z"></path></g></svg>.</span></div>

Discrete Dynamics in Nature and Society

fig2

Figure 2

Figure 2: Sharp Bounds on the Spectral Radii of Uniform Hypergraphs concerning Diameter or Clique Number 