Anzeige
Erschienen in:
01.07.2015
2-Disjoint-path-coverable panconnectedness of crossed cubes
Erschienen in: The Journal of Supercomputing | Ausgabe 7/2015
EinloggenAktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
Abstract
The crossed cube is a popular network topology because it possesses many attractive topological properties and its diameter is about half that of the hypercube. Typically, a network topology is modeled as a graph whose vertices and edges represent processors and communication links, respectively. We define a graph \(G\) to be \(2\)-disjoint-path-coverably \(r\)-panconnected for a positive integer \(r\) if for any four distinct vertices \(u,\, v,\, x\), and \(y\) of \(G\), there exist two vertex-disjoint paths \(P_1\) and \(P_2,\) such that (i) \(P_1\) joins \(u\) and \(v\) with length \(l\) for any integer \(l\) satisfying \(r \le l \le |V(G)| - r - 2\), and (ii) \(P_2\) joins \(x\) and \(y\) with length \(|V(G)| - l - 2\), where \(|V(G)|\) is the total number of vertices in \(G\). This property can be considered as an extension of both panconnectedness and connectivity. In this paper, we prove that the \(n\)-dimensional crossed cube is \(2\)-disjoint-path-coverably \(n\)-panconnected.