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On the difference between the (revised) Szeged index and the Wiener index of cacti
Klavžar, Sandi ; Li, Shuchao ; Zhang, Huihui
Povezan graf je kaktus, če je vsak njegov blok bodisi cikel bodisi povezava. Naj bo ▫$\mathscr{C}_n$▫ množica vseh kaktusov z ▫$n$▫ vozlišči, ki imajo vsaj en cikel daljši od 3, in naj bo ...▫$\mathscr{C}_{n,k}$▫ množica vseh kaktusov z ▫$n$▫ vozlišči, ki imajo natanko ▫$k\geq 1$▫ ciklov, kjer je ▫$n\geq 3k+1$▫. V tem članku so dokazane spodnje meje za razliko med (revidiranim) szegedskim indeksom in Wienerjevim indeksom grafov iz ▫$\mathscr{C}_n$▫ oz. iz ▫$\mathscr{C}_{n,k}$▫. Določene so najmanjše in druge najmanjše vrednosti za razliko med szegedskim indeksom in Wienerjevim indeksom za grafe iz ▫$\mathscr{C}_n$▫. Ocena za najmanjšo vrednost je izboljšana v dvodelnem primeru. Izpeljana je tudi spodnja meja na razliko med revidiranim szegedskim indeksom in Wienerjevim indeksom za grafe it ▫$\mathscr{C}_{n,k}$▫. V vseh primerih so določeni tudi vsi ekstremni grafi.
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