On the Graovac-Pisanski index of a graph

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Martin Knor Riste Škrekovski Aleksandra Tepeh


Let $G$ be a graph.Its Graovac-Pisanski index is\newline
\GP(G)=\frac{|V(G)|}{2|\Aut(G)|}\sum_{u\in V(G)}
where $\Aut(G)$ is the group
of automorphisms of $G$, and its Wiener index,
$W(G)$, is the sum of all
distances in $G$.
In the class of trees (unicyclic graphs) on $n$
vertices we find those with
the maximum value of Graovac-Pisanski index.
We show that the inequality $\GP(G)\le W(G)$ is
not true in general, but it
is true for trees.

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How to Cite
Knor, M., Škrekovski, R., & Tepeh, A. (2019). On the Graovac-Pisanski index of a graph. Acta Mathematica Universitatis Comenianae, 88(3), 867-870. Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1192/738