1Department of Mathematics, Slovak University of Technology in Bratislava, Faculty of Civil Engineering, Bratislava, Slovakia 2Faculty of Information Studies, Novo mesto & FMF, University of Ljubljana, Slovenia 3Faculty of Information Studies, Novo mesto & Faculty of Electrical Engineering and Computer Science, University of Maribor, Slovenia
Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 867-870
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Martin Knor; Riste Škrekovski; Aleksandra Tepeh; Martin Knor; Riste Škrekovski; Aleksandra Tepeh. On the Graovac-Pisanski index of a graph. Acta mathematica Universitatis Comenianae, Tome 88 (2019) no. 3, pp. 867-870. http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a78/
@article{AMUC_2019_88_3_a78,
author = {Martin Knor and Riste \v{S}krekovski and Aleksandra Tepeh and Martin Knor and Riste \v{S}krekovski and Aleksandra Tepeh},
title = { On the {Graovac-Pisanski} index of a graph},
journal = {Acta mathematica Universitatis Comenianae},
pages = {867--870},
year = {2019},
volume = {88},
number = {3},
url = {http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a78/}
}
TY - JOUR
AU - Martin Knor
AU - Riste Škrekovski
AU - Aleksandra Tepeh
AU - Martin Knor
AU - Riste Škrekovski
AU - Aleksandra Tepeh
TI - On the Graovac-Pisanski index of a graph
JO - Acta mathematica Universitatis Comenianae
PY - 2019
SP - 867
EP - 870
VL - 88
IS - 3
UR - http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a78/
ID - AMUC_2019_88_3_a78
ER -
%0 Journal Article
%A Martin Knor
%A Riste Škrekovski
%A Aleksandra Tepeh
%A Martin Knor
%A Riste Škrekovski
%A Aleksandra Tepeh
%T On the Graovac-Pisanski index of a graph
%J Acta mathematica Universitatis Comenianae
%D 2019
%P 867-870
%V 88
%N 3
%U http://geodesic.mathdoc.fr/item/AMUC_2019_88_3_a78/
%F AMUC_2019_88_3_a78
Let $G$ be a graph.Its Graovac-Pisanski index is\newline $$ \GP(G)=\frac{|V(G)|}{2|\Aut(G)|}\sum_{u\in V(G)} \sum_{\alpha\in\Aut(G)}\dist(u,\alpha(u)), $$ 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.
