Complexity of the Szeged index, edge orbits, and some nanotubical fullerenes
Alizadeh, Yaser ; Klavžar, Sandi
Naj bo ▫$I$▫ topološki indeks sumacijskega tipa. Potem je ▫$I$▫-zahtevnost ▫$C_I(G)$▫ grafa ▫$G$▫ število različnih prispevkov k ▫$I(G)$▫ v ustrezni sumacijski formuli. V tem članku raziskujemo ...zahtevnost ▫$C_{{\rm Sz}}(G)$▫, kjer je ▫${\rm Sz}$▫ dobro raziskovani Szegedski indeks. Naj bo ▫$O_e(G)$▫ (oz. ▫$O_v(G)$▫) število povezavnih (oz. vozliščnih) orbit grafa ▫$G$▫. Medtem ko za vsak graf ▫$G$▫ velja ▫$C_{{\rm Sz}}(G) \le O_e(G)$▫, je dokazano, da za vsak ▫$m \ge 1$▫ obstaja vozliščno-tranzitiven graf ▫$G_m$▫, za katerega velja ▫$C_{{\rm Sz}}(G_m) = O_e(G_m) = m$▫. Nadalje je pokazano, da za vsak ▫$1\le k\le m+1$▫ obstaja graf ▫$G_{m,k}$▫, za katerega velja ▫$C_{{\rm Sz}}(G_{m,k}) = O_e(G_{m,k}) = m$▫ in ▫$C_{W}(G_{m,k}) = O_v(G_{m,k}) = k$▫. Szegedska zahtevnost je določena za družino (5,0)-nanocevkastih fulerenov. Szegedski indeks je tudi primerjan s celotno ekscentričnostjo.
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