Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4630052 | Applied Mathematics and Computation | 2012 | 5 Pages |
Abstract
The first and the second Zagreb indices of a graph G=(V,E) are defined as M1(G)=âuâVdG(u)2 and M2(G)=âuvâEdG(u)dG(v), where dG(u) denotes the degree of a vertex u in G. It has recently been conjectured that M1(G)/|V|⩽M2(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.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Dragan StevanoviÄ,