Deficiency of forests
| Autor: | Javed Sana, Hussain Mujtaba, Riasat Ayesha, Kanwal Salma, Imtiaz Mariam, Ahmad M. O. |
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| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Open Mathematics, Vol 15, Iss 1, Pp 1431-1439 (2017) |
| Druh dokumentu: | article |
| ISSN: | 2391-5455 2017-0122 |
| DOI: | 10.1515/math-2017-0122 |
| Popis: | An edge-magic total labeling of an (n,m)-graph G = (V,E) is a one to one map λ from V(G) ∪ E(G) onto the integers {1,2,…,n + m} with the property that there exists an integer constant c such that λ(x) + λ(y) + λ(xy) = c for any xy ∈ E(G). It is called super edge-magic total labeling if λ (V(G)) = {1,2,…,n}. Furthermore, if G has no super edge-magic total labeling, then the minimum number of vertices added to G to have a super edge-magic total labeling, called super edge-magic deficiency of a graph G, is denoted by μs(G) [4]. If such vertices do not exist, then deficiency of G will be + ∞. In this paper we study the super edge-magic total labeling and deficiency of forests comprising of combs, 2-sided generalized combs and bistar. The evidence provided by these facts supports the conjecture proposed by Figueroa-Centeno, Ichishima and Muntaner-Bartle [2]. |
| Databáze: | Directory of Open Access Journals |
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