Frelih, Boštjan, matematika, 1976- ; Miklavič, Štefko
Naj bo ▫$n$▫ pozitivno celo število. Graf ▫$\Gamma$▫ premera najmanj ▫$n$▫ se imenuje ▫$n$▫-razdaljno-uravnotežen, če je za poljuben par vozlišč ▫$u, v$▫ grafa ▫$\Gamma$▫ na razdalji ▫$n$▫ število ...vozlišč, bližjih vozlišču ▫$u$▫ kot vozlišču ▫$v$▫, enako številu vozlišč, bližjih vozlišču ▫$v$▫ kot vozlišču ▫$u$▫. V tem članku obravnavamo ▫$n = 2$▫ (tj. obravnavamo 2-razdaljno-uravnotežene grafe). Pokažemo, da obstajajo 2-razdaljno-uravnoteženi grafi, ki niso 1-razdaljno-uravnoteženi (tj. razdaljno uravnoteženi). Karakteriziramo vse povezane 2-razdaljno-uravnotežene grafe, ki niso 2-povezani. Karakteriziramo tudi 2-razdaljno-uravnotežene grafe, ki jih lahko dobimo kot kartezične produkte ali leksikografske produkte dveh grafov.
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