On the embedding of cycles in pancake graphs

Kanevsky, Arkady; Feng, Chao

doi:10.1016/0167-8191(94)00096-s

Cited by 61 publications

(25 citation statements)

References 6 publications

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“…The main result of this paper is that BP n is Hamiltonian and weakly pancyclic: If n ≥ 2, BP n has a cycle of any length ℓ, where 8 ≤ ℓ ≤ 2 n n!. Our proof follows a similar technique to that in Kanevsky and Feng [18,Theorem 1], where the authors show that P n , for n ≥ 3, has cycles of length from 6 (the girth of P n ) up to n! − 2, and it is also Hamiltonian having a cycle of length n!.…”

Section: 3mentioning

confidence: 89%

Cycles in the burnt pancake graph

Blanco

Buehrle

Patidar

2019

Discrete Applied Mathematics

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The pancake graph Pn is the Cayley graph of the symmetric group Sn on n elements generated by prefix reversals. Pn has been shown to have properties that makes it a useful network scheme for parallel processors. For example, it is (n − 1)-regular, vertex-transitive, and one can embed cycles in it of length ℓ with 6 ≤ ℓ ≤ n!. The burnt pancake graph BPn, which is the Cayley graph of the group of signed permutations Bn using prefix reversals as generators, has similar properties. Indeed, BPn is n-regular and vertextransitive. In this paper, we show that BPn has every cycle of length ℓ with 8 ≤ ℓ ≤ 2 n n!. The proof given is a constructive one that utilizes the recursive structure of BPn.We also present a complete characterization of all the 8-cycles in BPn for n ≥ 2, which are the smallest cycles embeddable in BPn, by presenting their canonical forms as products of the prefix reversal generators.

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Section: 3mentioning

confidence: 89%

Cycles in the burnt pancake graph

Blanco

Buehrle

Patidar

2019

Discrete Applied Mathematics

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“…The ring structure is important for distributed computing, and its benefits can be found in [20]. Let us consider a problem about the cycle embeddings.…”

Section: Introductionmentioning

confidence: 99%

On embedding cycles into faulty twisted cubes

Yang

Tan

et al. 2006

Information Sciences

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“…It is easy to see that every edge-(bi)pancyclic graph is vertex-(bi)pancyclic and every vertex-(bi)pancyclic graph is (bi)pancyclic. Recently, pancyclicity is investigated in many interconnection networks such as star graphs [14], arrangement graphs [6], pancake graphs [16], cube-connected cycles [9], butterfly graphs [13], variants of hypercubes [7][8][9]19], Fibonacci cubes [2] and recursive circulants [3,4]. Pancyclicity is related to the cycle embedding problem.…”

Section: Introductionmentioning

confidence: 99%