For a simple graph ?$G$? with ?$n$? vertices and ?$m$? edges, the inequality ?$\frac{M_1(G)}{n} \le \frac{M_2(G)}{n}$?, where ?$M_1(G)$? and ?$M_2(G)$? are the first and the second Zagreb indices of ?$G$?, is known as Zagreb indices inequality. Recently Vukičević and Graovac Comparing Zagreb ?$M_1$? and ?$M_2$? indices for acyclic molecules, MATCH Commun. Math. Comput. Chem. 57 (2007), 587-590, and Caporossi, Hansen and Vukčević Comparing Zagreb indices of cyclic graphs, MATCH Commun. Math. Comput. Chem. 63 (2010), 441-451 proved that this inequality holds for trees and unicyclic graphs, respectively. Here, alternative and shorter proofs of these results are presented.

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URN

URN:NBN:SI:DOC-1YBY0OBF

COBISSID

16271449

Added

16.12.2021

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Citation

APA:

Andova, Vesna, Cohen, Nathann, Škrekovski, Riste (2012). A note on Zagreb indices inequality for trees and unicyclic graphs. Ars mathematica contemporanea, volume 5, issue 1, str. 73-76. URN:NBN:SI:DOC-1YBY0OBF from http://www.dlib.si

MLA:

Andova, Vesna, Cohen, Nathann, Škrekovski, Riste. "A note on Zagreb indices inequality for trees and unicyclic graphs." Ars mathematica contemporanea volume 5. issue 1 (2012) str. 73-76.
<http://www.dlib.si/?URN=URN:NBN:SI:DOC-1YBY0OBF>

Ars mathematica contemporanea
2008-
(Assembly record)