Seminar of Graph Theory - Martin Knor (11.10.2018)

Thursday 11.10.2018 at 9:50, Lecture room M/213

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Martin Knor (STU Bratislava):
Trees with the maximal value of Graovac-Pisanski index

Abstract:
Let $G$ be a graph. Its Graovac-Pisanski index is defined as $GP(G)=\frac{|V(G)|}{2|Aut(G)|}\sum_{u\in V(G)}\sum_{\apha\in Aut(G)}d_G(u,\alpha(u))$, where $Aut(G)$ is the group of automorphisms of $G$. It is easy to see that $G$ has the smallest Graovac-Pisanski index if its group of automorphisms is trivial, in which case $GP(G)=0$. The question is to find graphs with the largest value of Graovac-Pisanski index. We found graphs with the maximum value of Graovac-Pisanski index in the class of trees and in the class of unicyclic graphs.

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