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  • Graph classes (dis)satisfying the Zagreb indices inequality
    Andova, Vesna ; Cohen, Nathann ; Škrekovski, Riste
    Recently Hansen and Vukičević proved that the inequality ▫$M_1/n \leq M_2/m$▫, where ▫$M_1$▫ and ▫$M_2$▫ are the first and second Zagreb indices, holds for chemical graphs, and Vukičević and Graovac ... proved that this also holds for trees. In both works is given a distinct counterexample for which this inequality is false in general. Here, we present some classes of graphs with prescribed degrees, that satisfy ▫$M_1/n \leq M_2/m$▫. Namely every graph ▫$G$▫ whose degrees of vertices are in the interval ▫$[c,c + \lceil \sqrt c \, \rceil]$▫ for some integer ▫$c$▫, satisfies this inequality. In addition, we prove that for any ▫$\Delta \geq 5$▫, there is an infinite family of graphs of maximum degree ▫$\Delta$▫ such that the inequality is false.
    Vir: Match : communications in mathematical and in computer chemistry. - ISSN 0340-6253 (Vol. 65, no. 3, 2011, str. 647-658)
    Vrsta gradiva - e-članek
    Leto - 2011
    Jezik - angleški
    COBISS.SI-ID - 15894617

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