Authors: Stevanović, Dragan 
Title: Comparing the Zagreb indices of the NEPS of graphs
Journal: Applied Mathematics and Computation
Volume: 219
Issue: 3
First page: 1082
Last page: 1086
Issue Date: 15-Oct-2012
Rank: M21
ISSN: 0096-3003
DOI: 10.1016/j.amc.2012.07.014
Abstract: 
The first and the second Zagreb indices of a graph G =(V,E) are defined as M 1(G) = ∑ u∈Vd G(u) 2 and M 2(G) = ∑uv ∈Ed G(u)d G(v), where d G(u) denotes the degree of a vertex u in G. It has recently been conjectured that M 1(G)/|V|≤M 2(G)/|E|. Although some counterexamples have already been found, the question of characterizing graphs for which the inequality holds is left open. We show that this inequality is preserved under the NEPS of graphs, while its opposite is preserved under the direct product of graphs.
Keywords: Cartesian product of graphs | Direct product of graphs | Hansen- Vukičević conjecture | NEPS of graphs | The first Zagreb index | The second Zagreb index
Publisher: Elsevier
Project: Graph theory and mathematical programming with applications in chemistry and computer science 
Slovenian Agency for Research, program P1-0285

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