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].
@article{bwmeta1.element.doi-10_1515_math-2017-0122,
author = {Sana Javed and Mujtaba Hussain and Ayesha Riasat and Salma Kanwal and Mariam Imtiaz and M. O. Ahmad},
title = {Deficiency of forests},
journal = {Open Mathematics},
volume = {15},
year = {2017},
pages = {1431-1439},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_math-2017-0122}
}
Sana Javed; Mujtaba Hussain; Ayesha Riasat; Salma Kanwal; Mariam Imtiaz; M. O. Ahmad. Deficiency of forests. Open Mathematics, Tome 15 (2017) pp. 1431-1439. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_math-2017-0122/