Authors: Da Fonseca, Carlos
Ghebleh, Mohammad
Kanso, Ali
Stevanović, Dragan 
Title: Counterexamples to a conjecture on wiener index of common neighborhood graphs
Journal: Match
Volume: 72
Issue: 1
First page: 333
Last page: 338
Issue Date: 1-Jan-2014
Rank: M21
ISSN: 0340-6253
Abstract: 
For a simple graph G, the common neighborhood graph con(G) is the graph with the same vertex set as G, with two vertices adjacent in con(G) if they have a common neighbor in G. We describe here constructions of counterexamples to a conjecture of Knor et al. [MATCH Commun. Math. Comput. Chem. 72 (2014), 000-000] that there exists an absolute constant C such that for every graph G it holds that W(con(G)) ≤ C .W(G), where W(G) denotes the Wiener index of G.
Publisher: Faculty of Sciences, University of Kragujevac

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