Geodesic
Unicyclic graphs with the maximal value of Graovac-Pisanski index
Ars Mathematica Contemporanea, Tome 17 (2019) no. 2, pp. 455-466.

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Let G be a graph and let Γ be its group of automorphisms. Graovac-Pisanski index of G is GP(G) = |V(G)| / (2|Γ|) ∑u ∈ V(G) ∑α ∈ 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.
DOI : 10.26493/1855-3974.1925.57a
Keywords: Graovac-Pisanski index, modified Wiener index, unicyclic graphs 
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Martin Knor; Jozef Komorník; Riste Škrekovski; Aleksandra Tepeh. Unicyclic graphs with the maximal value of Graovac-Pisanski index. Ars Mathematica Contemporanea, Tome 17 (2019) no. 2, pp. 455-466. doi : 10.26493/1855-3974.1925.57a. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1925.57a/

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