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  • Product irregularity strength of certain graphs
    Anholcer, Marcin
    Consider a simple graph ▫$G$▫ with no isolated edges and at most one isolated vertex. A labeling ▫$w \colon E(G) \to \{1, 2, \dots,m\}$▫ is called product - irregular, if all product degrees ▫$pdG(v) ... = \prod_{e \ni v}w(e)$▫ are distinct. The goal is to obtain a product - irregular labeling that minimizes the maximal label. This minimal value is called the product irregularity strength and denoted ▫$ps(G)$▫. We give the exact values of ▫$ps(G)$▫ for several families of graphs, as complete bipartite graphs ▫$K_{m, n}$▫, where ▫$2 \le m \le n \le {m + 2 \choose 2}$▫, some families of forests, including complete ▫$d$▫-ary trees, and other graphs with ▫$\delta(G) = 1$▫.
    Vir: Ars mathematica contemporanea : special issue Bled'11 (Vol. 7, no. 1, 2014, str. 23-29)
    Vrsta gradiva - prispevek na konferenci ; neleposlovje za odrasle
    Leto - 2014
    Jezik - angleški
    COBISS.SI-ID - 16792153

    Povezava(-e):

    http://amc-journal.eu/index.php/amc/article/view/258/225
    Digitalna knjižnica Slovenije - dLib.si

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