Labeling the vertex amalgamation of graphs

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 of others. They also provide the basis for some new conjectures (and a weaker form of an old one) on labelings of 2-regular graphs.

show abstract

“…The following result found in [6] shows the relationship between a strongly felicitous graph and a graph admitting an α-valuation.…”

Section: Introductionmentioning

confidence: 79%

“…In [6], Figueroa-Centeno et al recently introduced a particular type of felicitous labelings, namely, strongly felicitous labelings. A felicitous labeling f of a graph G of size q is strongly felicitous if there exists an integer λ so that min…”

Section: Introductionmentioning

confidence: 99%

A magical approach to some labeling conjectures

Figueroa-Centeno¹,

Ichishima²,

Muntaner-Batle³

et al. 2011

Discuss. Math. Graph Theory

Self Cite

View full text Add to dashboard Cite

show abstract

“…On the other hand, Figueroa-Centeno et al [4] proved that every graph of order p and size q admitting an α-valuation is felicitous whenever q ≥ p − 1. This also allows us to find felicitous labelings of unicyclic graphs from the corresponding α-valuations of these.…”

Section: Discussionmentioning

confidence: 98%

Gracefully Cultivating Trees on a Cycle

Figueroa-Centeno

Ichishima

Muntaner-Batle

et al. 2015

Electronic Notes in Discrete Mathematics

Self Cite

View full text Add to dashboard Cite

“…Figueroa-Centeno et al [3] restricted the notion of felicitous graphs to obtain the definition of strongly felicitous graphs. A felicitous graph G with a felicitous labeling f is defined to be strongly felicitous if there exists an integer λ so that for each uv ∈ E (G) ,…”

Section: Relationships With Other Labelingsmentioning

confidence: 99%

On Partitional and Other Related Graphs

Ichishima

Oshima

2011

Math.Comput.Sci.

Self Cite

View full text Add to dashboard Cite

The partitional graphs, which are a subclass of the sequential graphs, were recently introduced by Ichishima and Oshima (Math Comput Sci 3:39-45, 2010), and the cartesian product of a partitional graph and K 2 was shown to be partitional, sequential, harmonious and felicitous. In this paper, we present some necessary conditions for a graph to be partitional. By means of these, we study the partitional properties of certain classes of graphs. In particular, we completely characterize the classes of the graphs B m and K m,2 × Q n that are partitional. We also establish the relationships between partitional graphs and graphs with strong α-valuations as well as strongly felicitous graphs.

show abstract

Labeling the vertex amalgamation of graphs

Cited by 9 publications

References 4 publications

A magical approach to some labeling conjectures

A magical approach to some labeling conjectures

Gracefully Cultivating Trees on a Cycle

On Partitional and Other Related Graphs

Contact Info

Product

Resources

About