2011
DOI: 10.7151/dmgt.1531
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A magical approach to some labeling conjectures

Abstract: In this paper, a complete characterization of the (super) edge-magic linear forests with two components is provided. In the process of establishing this characterization, the super edge-magic, harmonious, sequential and felicitous properties of certain 2-regular graphs are investigated, and several results on super edge-magic and felicitous labelings of unions of cycles and paths are presented. These labelings resolve one conjecture on harmonious graphs as a corollary, and make headway towards the resolution o… Show more

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Cited by 20 publications
(12 citation statements)
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“…Therefore, it seems to be a natural question to ask which 2-regular graphs are super edge-magic. This is what was in the minds of Figueroa-Centeno et al in [10] when they conjectured that the graph C m ∪ C n is super edge-magic if and only if m + n is odd and greater than 1. Holden et al went further into this conjecture, although they arrived to it from a different point of view, when they conjectured in [12] that all 2-regular graphs of odd order are strong vertex total magic, excluding C 3 ∪ C 4 , 3C 3 ∪ C 4 and 2C 3 ∪ C 5 , which is in fact equivalent to saying that they are super edge-magic.…”
Section: Super Edge-magic Labelings Of 2-regular Graphsmentioning
confidence: 65%
“…Therefore, it seems to be a natural question to ask which 2-regular graphs are super edge-magic. This is what was in the minds of Figueroa-Centeno et al in [10] when they conjectured that the graph C m ∪ C n is super edge-magic if and only if m + n is odd and greater than 1. Holden et al went further into this conjecture, although they arrived to it from a different point of view, when they conjectured in [12] that all 2-regular graphs of odd order are strong vertex total magic, excluding C 3 ∪ C 4 , 3C 3 ∪ C 4 and 2C 3 ∪ C 5 , which is in fact equivalent to saying that they are super edge-magic.…”
Section: Super Edge-magic Labelings Of 2-regular Graphsmentioning
confidence: 65%
“…Motivated by Conjecture 3.2, Figueroa-Centeno et al [17] showed that some 2-regular graphs with two components are SEM. They proved that 3 ∪…”
Section: Conjecture 32 [16] a 2-regular Graph Of Odd Order Is Sem Imentioning
confidence: 99%
“…Motivated by Conjecture 3.2 , Figueroa-Centeno et al [17] showed that some 2-regular graphs with two components are SEM. They proved that is SEM if and only if 4 is even, is SEM if and only if 5 is odd, is SEM if and only if 4 is even, and is SEM for any even 4 and odd 4 .…”
Section: The Semd Of 2 and Related Graphsmentioning
confidence: 99%
“…Based on the results of Theorem 1, the super edge-magic deficiency of H n is 0 for n = 3 and 4, and at least 1 for n ≥ 5. For n = 5, 6, 7, we could prove that µ s (H n ) = 1 by labeling the vertices (c; 6 ), and (c; x 1 , x 2 , x 3 , x 4 , x 5 , x 6 , x 7 ) with (1; 7, 5, 3, 6, 4), (2; 3, 1, 4, 8, 5, 6), and (2; 3, 1,4,8,5,9,6), respectively.…”
Section: Super Edge-magic Deficiency Of a Wheel Minus An Edgementioning
confidence: 99%