Pancyclicity of recursive circulant graphs

Araki, Tomoyuki; Shibata, Yukio

doi:10.1016/s0020-0190(01)00226-5

Cited by 41 publications

(36 citation statements)

References 7 publications

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“…They were not particularly interested in Cayley graphs, but their results include special Cayley graphs on abelian groups. Araki and Shibata [3] showed that a special class of circulant graphs, called recursive circulant graphs, are pancyclic and have odd length cycles of all possible lengths. Araki [2] then extended the results to edge-pancyclic.…”

Section: Theorem 1 If X Is a Connected Circulant Graph Of Order N Anmentioning

confidence: 99%

Pancyclicity and Cayley Graphs on Abelian Groups

Alspach

Bendit

Maitland

2012

Journal of Graph Theory

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Section: Theorem 1 If X Is a Connected Circulant Graph Of Order N Anmentioning

confidence: 99%

Pancyclicity and Cayley Graphs on Abelian Groups

Alspach

Bendit

Maitland

2012

Journal of Graph Theory

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“…In fact, these notions have been investigated in the context of some other networks, for example, in recursive circulant networks [9,24,124], Butterfly networks [25,93,140], cubeconnected cycle networks [58], hypercube-like networks [76,86,123,125], and so on.…”

Section: Remarks and Commentsmentioning

confidence: 99%

Survey on path and cycle embedding in some networks

2009

Front. Math. China

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To find a cycle (resp. path) of a given length in a graph is the cycle (resp. path) embedding problem. To find cycles of all lengths from its girth to its order in a graph is the pancyclic problem. A stronger concept than the pancylicity is the panconnectivity. A graph of order n is said to be panconnected if for any pair of different vertices x and y with distance d there exist xy-paths of every length from d to n. The pancyclicity or the panconnectivity is an important property to determine if the topology of a network is suitable for some applications where mapping cycles or paths of any length into the topology of the network is required. The pancyclicity and the panconnectivity of interconnection networks have attracted much research interest in recent years. A large amount of related work appeared in the literature, with some repetitions. The purpose of this paper is to give a survey of the results related to these topics for the hypercube and some hypercube-like networks.

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“…In [2], the authors consider pancyclicity of recursive circulants. Theorem 1.1 [2]. Let 1 c d. The purpose of this paper is to study edge-pancyclicity of recursive circulants and improve the result by showing that the class of these graphs contains edge-pancyclic or nearly edge-pancyclic graphs, that is, these graphs have the property of edge-pancyclicity except for short odd cycles.…”

Section: Introductionmentioning

confidence: 99%

Edge-pancyclicity of recursive circulants

Araki

2003

Information Processing Letters

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Pancyclicity of recursive circulant graphs

Cited by 41 publications

References 7 publications

Pancyclicity and Cayley Graphs on Abelian Groups

Pancyclicity and Cayley Graphs on Abelian Groups

Survey on path and cycle embedding in some networks

Edge-pancyclicity of recursive circulants

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