Medianski in kvazimedianski direktni produkti grafov

Median 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 ▫$K_3 times K_3$▫.Karakterizirani so tisti medianski grafi, ki so direktni produkt grafov z vsaj tremi točkami. Poleg nekaj pogostih primerov je dokazano, da je komponenta grafa ▫$G times K_3$▫ medianska natanko tedaj, ko je ▫$G$▫ drevo, v katerem je razdalja med poljubnima točkama stopnje vsaj tri sodo število. Dokazanih je tudi nekaj delnih rezultatov o medianskih grafih oblike ▫$G times K_2$▫. Nazadnje je dokazano, da je ▫$K_3 times K_3$▫ edini nedvodelni kvazimedianski direktni produkt