Hyper hamiltonian laceability of Cayley graphs generated by transpositions

Araki, Tomoyuki

doi:10.1002/net.20126

Cited by 36 publications

(28 citation statements)

References 15 publications

(22 reference statements)

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“…Older research on this include [31,33]. Recently, [2,32,30] studied them from the point of view of interconnection networks. The generalization is to replace the generating set {(1, 2), (1, 3), .…”

Section: Cayley Graphs Generated By 2-treesmentioning

confidence: 99%

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A kind of conditional vertex connectivity of Cayley graphs generated by 2-trees

Cheng

Lipták

Yang

et al. 2011

Information Sciences

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Section: Cayley Graphs Generated By 2-treesmentioning

confidence: 99%

“…For example (12) (34)(567)(8) is a cycle decomposition and its rearrangement representation is [2,1,4,3,6,7,5,8].…”

Section: Cayley Graphs Generated By 2-treesmentioning

confidence: 99%

A kind of conditional vertex connectivity of Cayley graphs generated by 2-trees

Cheng

Lipták

Yang

et al. 2011

Information Sciences

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“…Two permutations are adjacent if one can be obtained from the other by either a 2-exchange or a 3-rotation. A 2-exchange interchanges the symbols in positions 1 and 2 (that is, corresponding to the center edge (1,2) in Figure 1.) A 3-rotation rotates the symbols in the positions labelled by the vertices of a triangle, that is, the triangle with vertices 1, 2 and k for some k ∈ {3, 4, .…”

Section: Alternating Group Graphs and Split-starsmentioning

confidence: 99%

“…They are Cayley graphs generated by a special set of transpositions. In fact, many of their properties are shared by Cayley graphs generated by any set of transpositions, see, for example, Araki [2]. In [8], the matching preclusion problem for these graphs are solved.…”

Section: Cayley Graphs Generated By 3-cyclesmentioning

confidence: 99%

Matching Preclusion for Alternating Group Graphs and Their Generalizations

Cheng

Lesniak

Lipman

et al. 2008

Int. J. Found. Comput. Sci.

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The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. In this paper, we find this number for the alternating group graphs, Cayley graphs generated by 2-trees and the (n, k)-arrangement graphs. Moreover, we classify all the optimal solutions. . Downloaded from www.worldscientific.com by UNIVERSITY OF AUCKLAND LIBRARY -SERIALS UNIT on 02/03/15. For personal use only. 1414 E. Cheng et al. then it has an even number of vertices; if a graph has an almost-perfect matching, then it has an odd number of vertices. The matching preclusion number of a graph G, denoted by mp(G), is the minimum number of edges whose deletion leaves the resulting graph without a perfect matching or almost-perfect matching. Any such optimal set is called an optimal matching preclusion set. We define mp(G) = 0 if G has neither a perfect matching nor an almost-perfect matching. This concept of matching preclusion was introduced by Brigham, Harary, Violin and Yellen [5]. They introduced this concept as a measure of robustness in the event of edge failure in interconnection networks, as well as a theoretical connection to conditional connectivity, "changing and unchanging of invariants" and extremal graph theory. We refer the readers to [5] for details and additional references. In [5], the matching preclusion number was determined for three classes of graphs, namely, the complete graphs, the complete bipartite graphs and the hypercubes; in addition, all the optimal solutions were found. Useful distributed processor architectures offer the advantage of improved connectivity and reliability. An important component of such a distributed system is the system topology, which defines the inter-processor communication architecture. In the area of interconnection networks, hypercubes are classical. In the late 1980s and early 1990s, the star graphs (Akers, Harel and Krishnamurthy [1]) and the alternating group graphs (Jwo, Lakshmibarahan and Dhall [12]) were introduced as better alternatives than the hypercubes. Indeed, they have shown to be superior to the hypercubes in many ways. Later, two generalizations were introduced, namely, the (n, k)-star graphs (Chiang and Chen [9]) generalizing the star graphs and the arrangement graphs (Day and Tripathi [10]) generalizing both the star graphs and the alternating group graphs. They formed the core classes of interconnection networks. These networks have since generated a considerable amount of research including fault tolerant routings, strong connectivity properties, various Hamiltonian properties, broadcasting, orientation, and embedding. In certain applications, every vertex requires a special partner at any given time and the matching preclusion number measures the robustness of this requirement in the event of link failures as indicated in [5]. Hence in these interconnection networks, it is desirable to have the property that the only optimal matching preclusion sets are those whose ele...

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“…Most of the research is still concentrated on the star graphs. Recently, [3] rejuvenated the interest in another class of graphs that is a common generalization of the star graphs and bubble sort graphs [2] studied in [33]. This is the class of Cayley graphs generated by transpositions.…”

Section: Introductionmentioning

confidence: 99%