Unicyclic graphs with the maximal value of Graovac-Pisanski index

Martin Knor, Jozef Komorník, Riste Škrekovski, Aleksandra Tepeh

Abstract


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.


Keywords


Graovac-Pisanski index, modified Wiener index, unicyclic graphs

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DOI: https://doi.org/10.26493/1855-3974.1925.57a

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications