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|Title: ||The Panpositionable Panconnectedness of Augmented Cubes|
|Authors: ||龔自良;Kung, Tzu-Liang;Kueng, Tz-Liang|
|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  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.
|Relation: ||INFORMATION SCIENCES|
|Appears in Collections:||[資訊工程學系] 期刊論文|
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