Median and quasi-median direct products of graphsBrešar, Boštjan (Avtor) Jha, Pranava (Avtor) Klavžar, Sandi (Avtor) Zmazek, Blaž (Avtor) mathematicsgraph theorymedian graphdirect productquasi-median graphisometric embeddingsconvexityMedian graphs are characterized among direct products of graphs on at least three vertices. Beside some trivial cases, it is shown that one component of ▫$G \times P_3$▫ is median if and only if ▫$G$▫ is a tree in that the distance between any two vertices of degree at least 3 is even. In addition, some partial results considering median graphs of the form ▫$G \times K_2$▫ are proved, and it is shown that the only nonbipartite quasi-median direct product is ▫$K_3 \times K_3$▫.20052017-03-31 11:36:33Neznano65340ISSN: 1234-3099UDK: 519.17OceCobissID: 7487065COBISS_ID: 13477721ISSN pri članku: 1234-3099NUK URN: URN:SI:UM:DK:SAQHJXMPsl