The periphery graph of a median graphBrešar, Boštjan (Avtor) Changat, Manoj (Avtor) Subhamathi, Ajitha R. (Avtor) Tepeh, Aleksandra (Avtor) mathematicsgraph theorymedian graphCartesian productgeodesicperipheryperipheral expansionThe 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.University of Zielona Góra20102017-03-31 14:35:28Znanstveno delo65354sl