Regular connected bipancyclic spanning subgraphs of hypercubes

Mane, S. A.; Waphare, B. N.

doi:10.1016/j.camwa.2011.08.071

Cited by 14 publications

(10 citation statements)

References 22 publications

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“…For the general case, Mane and Waphare [12] proved that Q n contains a kregular, k-connected, bipancyclic subgraph on 2 n vertices (also see [1,3,15]). We strengthened this result by proving that 2 n can be replaced by 2 m with k ≤ m ≤ n or by 2 m + 2 m−1 with k ≤ m ≤ n − 1.…”

Section: Theorem 11 ([2]mentioning

confidence: 99%

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On 4-regular 4-connected bipancyclic subgraphs of hypercubes

Borse

Shaikh

2017

Discrete Math. Algorithm. Appl.

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We consider the problem of determining the possible orders for k-regular, k-connected and bipancyclic subgraphs of the hypercube Qn. For k = 2 and k = 3, the solution to the problem is known. In this paper, we solve the problem for k = 4 by proving that Qn has a 4-regular, 4-connected and bipancyclic subgraph on l vertices if and only if l = 16 or l is an even integer such that 24 ≤ l ≤ 2 n . Further, by improving a result of Ramras, we prove that a k-regular subgraph of Qn is either isomorphic to Q k or has at least 2 k + 2 k−1 vertices. We also improve a result of Mane and Waphare regarding the existence of a k-regular, k-connected and bipancyclic subgraph of Qn. Some applications of our results are given.

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Section: Theorem 11 ([2]mentioning

confidence: 99%

“…Therefore, we get the following result. [12] which states that the hypercube Q n has a k-regular, k-connected and bipancyclic subgraph on 2 n vertices for 3 ≤ k ≤ n.…”

Section: Lemma 24 ([12]mentioning

confidence: 99%

On 4-regular 4-connected bipancyclic subgraphs of hypercubes

Borse

Shaikh

2017

Discrete Math. Algorithm. Appl.

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“…In particular, the embedding of linear arrays and rings in a faulty interconnection network is of great significance. For example, path embedding in a faulty n-cube was addressed in [13,19,25]. However, one should notice that each component of a network may not be equally reliable.…”

Section: Introductionmentioning

confidence: 99%

Multiple regular graph embeddings into a hypercube with unbounded expansion

Lin

2013

Applied Mathematics and Computation

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“…The connectivity of a network gives the minimum cost to disrupt the network. Regular subgraphs, bipancyclicity, and connectivity properties of hypercubes are well studied in the literature [2][3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

“…Suppose 3 ≤ ≤ . Mane and Waphare [4] proved that contains a spanning -regular, -connected, bipancyclic subgraph. So the natural question arises; what are the other possible orders existing forregular, -connected and bipancyclic subgraphs of ?…”

Section: Introductionmentioning

confidence: 99%