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Regular maps with nilpotent automorphism groups
SYS 0194662 LBL -----naa--22--------450- 005 20231211111734.4 014 $a 000307865600021 $2 WOS CC. SCIE 014 $a 2-s2.0-84863828494 $2 SCOPUS 017 70
$a 10.1016/j.ejc.2012.06.001 $2 DOI 100 $a 20140217d2012 m y-slo-03 ----ba 101 0-
$a eng 102 $a GB 200 1-
$a Regular maps with nilpotent automorphism groups $f Aleksander Malnic, Roman Nedela, Martin Škoviera 330 $a We study regular maps with nilpotent automorphism groups in detail. We prove that every nilpotent regular map decomposes into a direct product of maps H x K, where Aut (H) is a 2-group and K is a map with a single vertex and an odd number of semiedges. Many important properties of nilpotent maps follow from this canonical decomposition, including restrictions on the valency, covalency, and the number of edges. We also show that, apart from two well-defined classes of maps on at most two vertices and their duals, every nilpotent regular map has both its valency and covalency divisible by 4. Finally, we give a complete classification of nilpotent regular maps of nilpotency class 2. 463 -1
$1 001 umb_un_cat*0309648 $1 011 $a 0195-6698 $1 011 $a 1095-9971 $1 200 1 $a European Journal of Combinatorics $v Vol. 33, no. 8 (2012), pp. 1974-1986 $1 210 $a London $c Academic Press $d 2012 606 0-
$3 umb_un_auth*0036218 $a matematika $X mathematics 606 0-
$3 umb_un_auth*0039537 $a grafy $X charts $X graphs 606 0-
$3 umb_un_auth*0125065 $a regulárne mapy 606 0-
$3 umb_un_auth*0116334 $a regular maps 615 $n 51 $a Matematika $2 konspekt 675 $a 51 $v 3. $z slo 700 -0
$3 umb_un_auth*0013387 $a Malnič $b Aleksander $9 34 $4 070 701 -0
$3 umb_un_auth*0001645 $a Nedela $b Roman $p UMBFP12 $9 33 $f 1960- $4 070 $T Inštitút matematiky a informatiky 701 -0
$3 umb_un_auth*0022262 $a Škoviera $b Martin $9 33 $4 070 801 -0
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Number of the records: 1