In the mathematical field of graph theory , a graph G is symmetric (or arc-transitive ) if, given any two pairs of adjacent vertices u 1 — v 1 and u 2 — v 2 of G , there is an automorphism
25-845: (Redirected from XXXIX ) "Thirty-nine" redirects here. For the South Korean drama series, see Thirty-Nine . Natural number ← 38 39 40 → ← 30 31 32 33 34 35 36 37 38 39 → List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 → Cardinal thirty-nine Ordinal 39th (thirty-ninth) Factorization 3 × 13 Divisors 1, 3, 13, 39 Greek numeral ΛΘ´ Roman numeral XXXIX Binary 100111 2 Ternary 1110 3 Senary 103 6 Octal 47 8 Duodecimal 33 12 Hexadecimal 27 16 39 ( thirty-nine )
50-515: A symmetric graph with 39 edges. In science [ edit ] The atomic number of yttrium Astronomy [ edit ] Messier object Open Cluster M39 , a magnitude 5.5 open cluster in the constellation Cygnus The New General Catalogue object NGC 39 , a spiral galaxy in the constellation Andromeda In religion [ edit ] The number of the 39 categories of activity prohibited on Shabbat according to Halakha The number of mentions of work or labor in
75-399: A distance of 1 apart), the definition covers two pairs of vertices, each the same distance apart. Such graphs are automatically symmetric, by definition. A t -arc is defined to be a sequence of t + 1 vertices, such that any two consecutive vertices in the sequence are adjacent, and with any repeated vertices being more than 2 steps apart. A t -transitive graph is a graph such that
100-468: A further example, semi-symmetric graphs are edge-transitive and regular , but not vertex-transitive. Every connected symmetric graph must thus be both vertex-transitive and edge-transitive, and the converse is true for graphs of odd degree. However, for even degree, there exist connected graphs which are vertex-transitive and edge-transitive, but not symmetric. Such graphs are called half-transitive . The smallest connected half-transitive graph
125-449: A strong condition, and such graphs are rare enough to be listed. They all have an even number of vertices. The Foster census and its extensions provide such lists. The Foster census was begun in the 1930s by Ronald M. Foster while he was employed by Bell Labs , and in 1988 (when Foster was 92 ) the then current Foster census (listing all cubic symmetric graphs up to 512 vertices) was published in book form. The first thirteen items in
150-399: A symmetric graph without isolated vertices must also be vertex-transitive . Since the definition above maps one edge to another, a symmetric graph must also be edge-transitive . However, an edge-transitive graph need not be symmetric, since a—b might map to c—d , but not to d—c . Star graphs are a simple example of being edge-transitive without being vertex-transitive or symmetric. As
175-422: Is Holt's graph , with degree 4 and 27 vertices. Confusingly, some authors use the term "symmetric graph" to mean a graph which is vertex-transitive and edge-transitive, rather than an arc-transitive graph. Such a definition would include half-transitive graphs, which are excluded under the definition above. A distance-transitive graph is one where instead of considering pairs of adjacent vertices (i.e. vertices
200-411: Is a 2022 South Korean television series directed by Kim Sang-ho and starring Son Ye-jin , Jeon Mi-do , and Kim Ji-hyun . The series remake of Chinese Drama Nothing But Thirty revolves around the life, friendship, romances, and love of three friends who are about to turn forty. It premiered on JTBC on February 16, 2022, and aired every Wednesday and Thursday at 22:30 ( KST ) for 12 episodes. It
225-740: Is a song by the Cure on their album Bloodflowers "39" is a song by Tenacious D on their album Rize of the Fenix " '39 " is a song by Queen on their album A Night at the Opera The book series The 39 Clues revolves around 39 clues hidden around the world Glorious 39 is a 2009 drama film set at the beginning of World War II In the CBS reality show Survivor , contestants compete for 39 days The number of episodes done during its one season in 1955–1956 of The Honeymooners television series
250-920: Is available for streaming on Netflix . The last episode of the series logged its highest ratings national wide: of 8.1%. Additionally, it was listed for four weeks in the Global Top 10 weekly list of the most-watched international Netflix TV shows as of April 3. In April 2021, it was announced that Son Ye-jin and Jeon Mi-do were in talks to appear in Thirty-Nine , a 12-episode mini-series co-produced by Lotte Cultureworks and JTBC Studio. Son confirmed her appearance in June 2021, while Jeon and Kim Ji-hyun confirmed in August. Thirty-Nine marks Son's return to JTBC after three years; she last appeared in JTBC's 2018 TV series Something in
275-480: Is commonly referred to as the " Classic 39 " Japanese wordplay and slang: Internet chat slang for "Thank You" when written with numbers: 3 ( 三 , san ) and 9 ( 九 , kyū ) . 39 has been associated with the virtual singer Hatsune Miku because the written form of "Mi" ( ミ ) and the phonic pronunciation of "ku" ( ク ) have similarity to the numbers 3 ( 三 , san ) and 9 ( 九 , kyū ) . History [ edit ] The number of signers to
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#1733085944791300-482: Is the natural number following 38 and preceding 40 . In mathematics [ edit ] [REDACTED] The F26A graph has 39 edges, all equivalent. 39 is the 12th distinct semiprime and the 4th in the (3.q) family. It is the last member of the third distinct semiprime pair ( 38 ,39). 39 has an aliquot sum of 17 , which is a prime. 39 is the 4th member of the 17 -aliquot tree within an aliquot sequence of one composite numbers (39, 17 , 1 ,0) to
325-400: Is the smallest natural number which has three partitions into three parts which all give the same product when multiplied: {25, 8, 6}, {24, 10, 5}, {20, 15, 4}. 39 is a Perrin number , coming after 17, 22, 29 (it is the sum of the first two mentioned). Since the greatest prime factor of 39 + 1 = 1522 is 761, which is more than 39 twice, 39 is a Størmer number . The F26A graph is
350-477: Is zero" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation . Retrieved 2016-05-31 . ^ "Sloane's A001608 : Perrin sequence" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation . Retrieved 2016-05-31 . ^ "Sloane's A005528 : Størmer numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation . Retrieved 2016-05-31 . ^ Specktor, Brandon (2 November 2017). "Here's Why
375-1153: The Gulf War in 1991 The code for international direct-dialed phone calls to Italy Pier 39 in San Francisco The number of the French department Jura In Afghanistan , the number 39 is considered unlucky, due to the belief that it is associated with pimps . See Curse of 39 . The bowling lane normally consists of 39 wooden boards See also [ edit ] List of highways numbered 39 References [ edit ] ^ Sloane, N. J. A. (ed.). "Sequence A001358" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. ^ Sloane, N. J. A. (ed.). "Sequence A001748" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation. ^ "Sloane's A082897 : Perfect totient numbers" . The On-Line Encyclopedia of Integer Sequences . OEIS Foundation . Retrieved 2016-05-31 . ^ "Sloane's A028442 : Numbers n such that Mertens' function
400-773: The Torah The actual number of lashes given by the Sanhedrin to a person meted the punishment of 40 lashes The number of books in the Old Testament according to Protestant canon The number of statements on Anglican Church doctrine, Thirty-Nine Articles In other fields [ edit ] Arts and entertainment [ edit ] In the title of the John Buchan novel and subsequent films (one by Alfred Hitchcock ), The Thirty-Nine Steps The age American comedian Jack Benny claimed to be for more than 40 years "39"
425-553: The United States Constitution , out of 55 members of the Philadelphia Convention delegates The traditional number of times citizens of Ancient Rome hit their slaves when beating them, referred to as " Forty save one " The duration, in nanoseconds, of the nuclear reaction in the largest nuclear explosion ever performed ( Tsar Bomba ) The number of Scud missiles which Iraq fired at Israel during
450-11586: The Number "39" Means "Thank You" in Japan" . Reader's Digest . Retrieved 23 March 2021 . ^ "3/9 Marks Happy "Miku" & "Zaku" Day In Japan, Fan Artists Mark The Occasion" . Crunchyroll . Retrieved 2024-08-15 . ^ "Loya jirga: Afghan elders reject 'pimp's number 39' " . BBC News . 17 November 2011 . Retrieved 3 May 2012 . v t e Integers 0s -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100s 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200s 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300s 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400s 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500s 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600s 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700s 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800s 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900s 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 ≥ 1000 1000 2000 3000 4000 5000 6000 7000 8000 9000 10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 90,000 100,000 1,000,000 10,000,000 100,000,000 1,000,000,000 Retrieved from " https://en.wikipedia.org/w/index.php?title=39_(number)&oldid=1244213181 " Category : Integers Hidden categories: Articles with short description Short description matches Wikidata Articles containing Japanese-language text Thirty-Nine Thirty-Nine ( Korean : 서른, 아홉 ; RR : Seoreun, Ahop )
475-524: The Prime in the 17 -aliquot tree. It is a perfect totient number . 39 is the sum of five consecutive primes (3 + 5 + 7 + 11 + 13) and also is the product of the first and the last of those consecutive primes. Among small semiprimes only three other integers (10, 155, and 371) share this attribute. 39 also is the sum of the first three powers of 3 (3 + 3 + 3). Given 39, the Mertens function returns 0 . 39
500-519: The Rain . Filming began in August 2021. On January 12, 2022, photos from the script reading were published. Symmetric graph such that In other words, a graph is symmetric if its automorphism group acts transitively on ordered pairs of adjacent vertices (that is, upon edges considered as having a direction). Such a graph is sometimes also called 1-arc -transitive or flag-transitive . By definition (ignoring u 1 and u 2 ),
525-424: The automorphism group acts transitively on t -arcs , but not on ( t + 1 )-arcs . Since 1-arcs are simply edges, every symmetric graph of degree 3 or more must be t -transitive for some t , and the value of t can be used to further classify symmetric graphs. The cube is 2-transitive , for example. Note that conventionally the term "symmetric graph" is not complementary to the term " asymmetric graph ," as
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#1733085944791550-457: The cube to n dimensions gives the hypercube graphs (with 2 vertices and degree n). Similarly extension of the octahedron to n dimensions gives the graphs of the cross-polytopes , this family of graphs (with 2n vertices and degree 2n-2) are sometimes referred to as the cocktail party graphs - they are complete graphs with a set of edges making a perfect matching removed. Additional families of symmetric graphs with an even number of vertices 2n, are
575-409: The evenly split complete bipartite graphs K n,n and the crown graphs on 2n vertices. Many other symmetric graphs can be classified as circulant graphs (but not all). The Rado graph forms an example of a symmetric graph with infinitely many vertices and infinite degree. Combining the symmetry condition with the restriction that graphs be cubic (i.e. all vertices have degree 3) yields quite
600-419: The latter refers to a graph that has no nontrivial symmetries at all. Two basic families of symmetric graphs for any number of vertices are the cycle graphs (of degree 2) and the complete graphs . Further symmetric graphs are formed by the vertices and edges of the regular and quasiregular polyhedra: the cube , octahedron , icosahedron , dodecahedron , cuboctahedron , and icosidodecahedron . Extension of
625-601: The list are cubic symmetric graphs with up to 30 vertices (ten of these are also distance-transitive ; the exceptions are as indicated): Other well known cubic symmetric graphs are the Dyck graph , the Foster graph and the Biggs–;Smith graph . The ten distance-transitive graphs listed above, together with the Foster graph and the Biggs–Smith graph , are the only cubic distance-transitive graphs. The vertex-connectivity of
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