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    ASIA unversity > 資訊學院 > 資訊工程學系 > 期刊論文 >  Item 310904400/18680


    Please use this identifier to cite or link to this item: http://asiair.asia.edu.tw/ir/handle/310904400/18680


    Title: The Panpositionable Panconnectedness of Augmented Cubes
    Authors: 龔自良;Kung, Tzu-Liang;Kueng, Tz-Liang
    Contributors: 資訊工程學系
    Date: 2010-10
    Issue Date: 2012-11-26 13:56:59 (UTC+8)
    Abstract: A graph G is panconnected if, for any two distinct vertices x and y of G, it contains an [x, y]-
    path of length l for each integer l satisfying dG(x,y) 6 l 6 jV(G)j 1, where dG(x,y) denotes
    the distance between vertices x and y in G, and V(G) denotes the vertex set of G. For insight
    into the concept of panconnectedness, we propose a more refined property, namely panpositionable
    panconnectedness. Let x, y, and z be any three distinct vertices in a graph G.
    Then G is said to be panpositionably panconnected if for any dG(x, z) 6 l1 6 jV(G)j
    dG(y, z) 1, it contains a path P such that x is the beginning vertex of P, z is the (l1 + 1)th
    vertex of P, and y is the (l1 + l2 + 1)th vertex of P for any integer l2 satisfying dG(y, z) 6
    l2 6 jV(G)j l1 1. The augmented cube, proposed by Choudum and Sunitha [6] to be an
    enhancement of the n-cube Qn, not only retains some attractive characteristics of Qn but
    also possesses many distinguishing properties of which Qn lacks. In this paper, we investigate
    the panpositionable panconnectedness with respect to the class of augmented cubes.
    As a consequence, many topological properties related to cycle and path embedding in augmented
    cubes, such as pancyclicity, panconnectedness, and panpositionable Hamiltonicity,
    can be drawn from our results.
    2
    Relation: INFORMATION SCIENCES
    Appears in Collections:[資訊工程學系] 期刊論文

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