Sana Javed, Mujtaba Hussain, Ayesha Riasat, Salma Kanwal, Mariam Imtiaz, M. O. Ahmad
December 9, 2017

### Abstract

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 μ s ( 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].