The power of digraph products applied to labelings

Ichishima, Rikio; López, Susana-Clara; Muntaner-Batle, Francesc A.; Rius-Font, Miquel

doi:10.1016/j.disc.2011.08.025

Cited by 17 publications

(16 citation statements)

References 18 publications

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“…In all the results involving the ⊗ h -product, since the very beginning, it seems to be a constant to use super edge-magic labeled graphs as the second factor of the product, or at least graphs that in a way or another come from super edge-magic graphs [10,15,18]. The power of this section lies in the fact that it allows us to use other types of labeled graphs as a second factor of the product and this allows to refresh the ways of attacking old famous problems in the subject of graph labelings as we will in the next lines.…”

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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“…Super edge-magic labelings are of importance among graph labelings due to the great amount of relations that they have with other labelings (see [7,11,13,16,17]).…”

Section: Dual Shuffle Primesmentioning

confidence: 99%

The Jumping Knight and Other (Super) Edge-Magic Constructions

2013

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Let G be a graph of order p and size q with loops allowed. A bijective function f : V (G) ∪ E(G) → {i} p+q i=1 is an edge-magic labeling of G if the sum f (u) + f (uv) + f (v) = k is independent of the choice of the edge uv. The constant k is called either the valence, the magic weight or the magic sum of the labeling f. If a graph admits an edge-magic labeling, then it is called an edge-magic graph. Furthermore, if the function f meets the extra condition that f (V (G)) = {i} p i=1 then f is called a super edge-magic labeling and G is called a super edge-magic graph. A digraph D admits a labeling, namely l, if its underlying graph, und(D) admits l. In this paper, we introduce a new construction of super edge-magic labelings which is related to the classical jump of the knight on the chess game. We also use super edge-magic labelings of digraphs together with a generalization of the Kronecker product in order to get edge-magic labelings of some families of graphs.

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“…In this proposed paper, for d ∈ {0, 1, 2, 3}, we find a super (b, d)-labeling of edge-antimagic total of the star for subdivided where q ≥ 5, and n ≥ 3 is odd. [12] detected the following bounds of lower and upper areas of the magic constant a for a specific subdivided stars subclass denoted by T (m, n, k): …”

Section: Description 21mentioning

confidence: 99%

“…• [12,13] called the star of subdivided T (m, n, k) as a three-path tree and proved that it is a super (b, 0)-EAT if m and n are odd functions with or [12] Verified that T (m, n, k) also admits a super (b, 0)-labeling of edge-antimagic total if m and n are odd functions with or .…”

Section: Description 21mentioning

confidence: 99%

Subdivided Stars Super (b, d) - Edge-Antimagic Total Graph Labelling

Mathew¹

2015

DJ JEAM

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In the existing method the authors assume that there admits in every tree a labeling of edgemagic total. The existing author proposed the speculations that every tree is a super (b, d)-graph of edge-antimagic total.In this proposed paper, we frame the subdivided star super (b, d)-edge-antimagic total labeling , n 5 , n 6 ..., n q ) for d ∈ {0, 1, 2}, where q ≥ 5, n s , 5 ≤ s≤ q and n ≥ 3 is odd.

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The power of digraph products applied to labelings

Cited by 17 publications

References 18 publications

A new labeling construction from the⊗h-product

A new labeling construction from the⊗h-product

The Jumping Knight and Other (Super) Edge-Magic Constructions

Subdivided Stars Super (b, d) - Edge-Antimagic Total Graph Labelling

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