20.500.12556/DKUM-65354 The periphery graph of a median graph Grafi periferij medianskega grafa The periphery graph of a median graph is the intersection graph of its peripheral subgraphs. We show that every graph without a universal vertex can be realized as the periphery graph of a median graph. We characterize those median graphs whose periphery graph is the join of two graphs and show that they are precisely Cartesian products of median graphs. Path-like median graphs are introduced as the graphs whose periphery graph has independence number 2, and it is proved that there are path-like median graphs with arbitrarily large geodetic number. Peripheral expansion with respect to periphery graph is also considered, and connections with the concept of crossing graph are established. Graf periferij medianskega grafa je presečni graf njegovih perifernih podgrafov. V članku pokažemo, da je vsak graf brez univerzalnih vozlišč mogoče realizirati kot graf periferij nekega medianskega grafa. Karakteriziramo tiste medianske grafe, katerih graf periferij je spoj dveh grafov in pokažemo, da so to natanko kartezični produkti medianskih grafov. Vpeljemo medianske grafe sorodne potem, ki so tisti medianski grafi, katerih neodvisnostno število grafa periferij je enako 2, ter pokažemo, da obstajajo medianski grafi sorodni potem s poljubno velikim geodetskim številom. Glede na grafe periferij je obravnavana periferna ekspanzija, pokažemo pa tudi povezavo s konceptom križnih grafov. mathematics graph theory median graph Cartesian product geodesic periphery peripheral expansion matematika teorija grafov medianski graf kartezični produkt periferija periferna ekspanzija true true true University of Zielona Góra Angleški jezik Slovenski jezik Znanstveno delo 2017-03-31 14:35:28 2017-03-31 14:36:26 2025-09-24 14:43:00 2019-07-11 15:15:34 2010 0 0 Str. 17-32 št. 1 Letn. 30 2010 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 2008-06-11 2009-01-05 1234-3099 519.17 7487065 15637081 1234-3099 URN:SI:UM:DK:D2OZSN9J Discussiones_Mathematicae_Graph_Theory_2010_Bresar_et_al._The_periphery_graph_of_a_median_graph.pdf Discussiones_Mathematicae_Graph_Theory_2010_Bresar_et_al._The_periphery_graph_of_a_median_graph.pdf 1 3E369953FC6F1AC9E804439E845A0BCC e00cd50cbcc2c0516d5e578ed9a8019c32ce738f5d0e2d210a5a5cd9e49a9063 0c14afe7-7c0e-11eb-bb7a-00155d0001ca https://dk.um.si/Dokument.php?lang=slv&id=110436 http://www.discuss.wmie.uz.zgora.pl/gt/index.php?doi=10.7151/dmgt.1473 1 https://dk.um.si/Dokument.php?lang=slv&id=110435 Fakulteta za naravoslovje in matematiko 0 0 0