Langford sequences and a product of digraphs

López, Susana-Clara; Muntaner-Batle, Francesc A.

doi:10.1016/j.ejc.2015.11.004

Cited by 7 publications

(6 citation statements)

References 22 publications

(42 reference statements)

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“…The lack of enumerative results involving graph labelings constitutes a big gap in the literature of graph labelings that this product has helped to fill enormously. Also further applications outside the world of graph labeling have been found for the ⊗ h -product, as for instance it introduces new ways to construct Skolem and Langford type sequences [13]. In summary, the ⊗-product constitutes a big breakthru into the world of graph labeling that allows to have a better and deeper understanding of the subject.…”

Section: The Main Resultsmentioning

confidence: 99%

A new labeling construction from the⊗h-product

Lpez

Muntaner-Batle

Prabu

2017

Discrete Mathematics

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The ⊗ h -product that refers the title was introduced in 2008 as a generalization of the Kronecker product of digraphs. Many relations among labelings have been obtained since then, always using as a second factor a family of super edge-magic graphs with equal order and size. In this paper, we introduce a new labeling construction by changing the role of the factors. Using this new construction the range of applications grows up considerably. In particular, we can increase the information about magic sums of cycles and crowns.

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Section: The Main Resultsmentioning

confidence: 99%

A new labeling construction from the⊗h-product

Lpez

Muntaner-Batle

Prabu

2017

Discrete Mathematics

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“…It seems highly likely that the bounds obtained in this paper apply to all pure, split, hooked and split-hooked Skolem sequences of sufficiently large orders. The recent paper [8] combines such bounds with graph labellings to generate Langford sequences. It seems likely that our new bounds can be combined with these techniques to generate improved estimates for the numbers of Langford sequences.…”

Section: Discussionmentioning

confidence: 99%

“…Corollary 3.2 gives the bound (6.492) 2t+1 when n = 7t + 3 and t ≡ 0 or 3 (mod 4), thereby dealing with n ≡ 3 or 24 (mod 28). The necessary and sufficient conditions on n for the existence of a split Skolem sequence of order n may be written as n ≡ 0, 3,4,7,8,11,12,15,16,19,20,23,24 or 27 (mod 28). For our example, we show how the bound may be extended to n ≡ 0 or 7 (mod 28).…”

Section: Skolem-type Sequencesmentioning

confidence: 99%

On the number of additive permutations and Skolem-type sequences

Donovan

Grannell

2017

Ars Math. Contemp.

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Cavenagh and Wanless recently proved that, for sufficiently large odd n, the number of transversals in the Latin square formed from the addition table for integers modulo n is greater than (3.246) n. We adapt their proof to show that for sufficiently large t the number of additive permutations on [−t, t] is greater than (3.246) 2t+1 and we go on to derive some much improved lower bounds on the numbers of Skolem-type sequences. For example, it is shown that for sufficiently large t ≡ 0 or 3 (mod 4), the number of split Skolem sequences of order n = 7t+3 is greater than (3.246) 6t+3. This compares with the previous best bound of 2 n/3 .

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“…The next result is an application of the ⊗ h -product to k-equitable digraphs. [22] to construct an exponential number of Langford sequences with certain orders and defects.…”

Section: The ⊗ H -Product Applied To Labelingsmentioning

confidence: 99%

(Di)graph products, labelings and related results

López

2017

Electronic Notes in Discrete Mathematics

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Gallian's survey shows that there is a big variety of labelings of graphs. By means of (di)graphs products we can establish strong relations among some of them. Moreover, due to the freedom of one of the factors, we can also obtain enumerative results that provide lower bounds on the number of nonisomorphic labelings of a particular type. In this paper, we will focus in three of the (di)graphs products that have been used in these duties: the ¿h-product of digraphs, the weak tensor product of graphs and the weak ¿h-product of graphs.Postprint (updated version

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Langford sequences and a product of digraphs

Cited by 7 publications

References 22 publications

A new labeling construction from the⊗h-product

A new labeling construction from the⊗h-product

On the number of additive permutations and Skolem-type sequences

(Di)graph products, labelings and related results

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