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Embedding of Supplementary Results in Strong EMT Valuations and Strength
- Source :
- Open Mathematics, Vol 17, Iss 1, Pp 527-543 (2019)
- Publication Year :
- 2019
- Publisher :
- De Gruyter, 2019.
-
Abstract
- A graph ℘ is said to be edge-magic total (EMT if there is a bijection Υ : V(℘) ∪ E(℘) → {1, 2, …, |V(℘) ∪ E(℘)|} s.t., Υ(υ) + Υ(υν) + Υ(ν) is a constant for every edge υν ∈ E(℘). An EMT graph ℘ will be called strong edge-magic total (SEMT) if Υ(V(℘)) = {1, 2, …, |V(℘)|}. The SEMT strength, sm(℘), of a graph ℘ is the minimum of all magic constants a(Υ), where the minimum runs over all the SEMT valuations of ℘, this minimum is defined only if the graph has at least one such SEMT valuation. Furthermore, the SEMT deficiency of a graph ℘, μs(℘), is either the minimum non-negative integer n such that ℘ ∪ nK1 is SEMT or +∞ if there will be no such integer n. In this paper, we will present the strong edge-magicness and deficiency of disjoint union of 2-sided generalized comb with bistar, path and caterpillar, moreover we will evaluate the SEMT strength for 2-sided generalized comb.
Details
- Language :
- English
- ISSN :
- 23915455
- Volume :
- 17
- Issue :
- 1
- Database :
- Directory of Open Access Journals
- Journal :
- Open Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.f5b98fac4d349638dd75b658fd860f9
- Document Type :
- article
- Full Text :
- https://doi.org/10.1515/math-2019-0044