Geodesic
The Gutman Index and the Edge-Wiener Index of Graphs with Given Vertex-Connectivity
Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 4, pp. 867-876

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The Gutman index and the edge-Wiener index have been extensively investigated particularly in the last decade. An important stream of re- search on graph indices is to bound indices in terms of the order and other parameters of given graph. In this paper we present asymptotically sharp upper bounds on the Gutman index and the edge-Wiener index for graphs of given order and vertex-connectivity κ, where κ is a constant. Our results substantially generalize and extend known results in the area.
Keywords: Gutman index, edge-Wiener index, vertex-connectivity 
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Mazorodze, Jaya Percival; Mukwembi, Simon; Vetrík, Tomáš. The Gutman Index and the Edge-Wiener Index of Graphs with Given Vertex-Connectivity. Discussiones Mathematicae. Graph Theory, Tome 36 (2016) no. 4, pp. 867-876. http://geodesic.mathdoc.fr/item/DMGT_2016_36_4_a7/