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- W205907742 abstract "This paper is the continuation of the research of the author and his colleagues of the {it canonical} decomposition of graphs. The idea of the canonical decomposition is to define the binary operation on the set of graphs and to represent the graph under study as a product of prime elements with respect to this operation. We consider the graph together with the arbitrary partition of its vertex set into $n$ subsets ($n$-partitioned graph). On the set of $n$-partitioned graphs distinguished up to isomorphism we consider the binary algebraic operation $circ_H$ ($H$-product of graphs), determined by the digraph $H$. It is proved, that every operation $circ_H$ defines the unique factorization as a product of prime factors. We define $H$-threshold graphs as graphs, which could be represented as the product $circ_{H}$ of one-vertex factors, and the threshold-width of the graph $G$ as the minimum size of $H$ such, that $G$ is $H$-threshold. $H$-threshold graphs generalize the classes of threshold graphs and difference graphs and extend their properties. We show, that the threshold-width is defined for all graphs, and give the characterization of graphs with fixed threshold-width. We study in detail the graphs with threshold-widths 1 and 2." @default.
- W205907742 created "2016-06-24" @default.
- W205907742 creator A5052456631 @default.
- W205907742 date "2010-11-22" @default.
- W205907742 modified "2023-09-27" @default.
- W205907742 title "H-product and the related dimension of graphs" @default.
- W205907742 hasPublicationYear "2010" @default.
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