Unicyclic graphs with the maximal value of Graovac-Pisanski index - Knor, Martin (Ars mathematica contemporanea, 2019)
Let ?$G$? be a graph and let ?$Γ$? be its group of automorphisms. Graovac-Pisanski index of ?$G$? is ?$GP(G) = \frac{|V(G)|}{2|Γ|} \sum_{u \in V(G)} \sum_{α \in Γ} d(u, α(u))$?, where ?$d(u, v)$? is the distance from ?$u$? to ?$v$? in ?$G$?. One can observe that ?$GP(G) = 0$? if ?$G$? has no nontrivial automorphisms, but it is not known which graphs attain the maximum value of Graovac-Pisanski index. In this paper we show that among unicyclic graphs on ?$n$? vertices the ?$n$?-cycle attains the maximum value of Graovac-Pisanski index.
Keywords: enociklični grafi; girth; Graovac-Pisanski indeks; Graovac-Pisanski index; modificirani Wienerjev indeks; modified Wiener index; unicyclic graphs