# Deficiency of forests

Sana Javed; Mujtaba Hussain; Ayesha Riasat; Salma Kanwal; Mariam Imtiaz; M. O. Ahmad

Open Mathematics (2017)

- Volume: 15, Issue: 1, page 1431-1439
- ISSN: 2391-5455

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topSana Javed, et al. "Deficiency of forests." Open Mathematics 15.1 (2017): 1431-1439. <http://eudml.org/doc/288340>.

@article{SanaJaved2017,

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 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].},

author = {Sana Javed, Mujtaba Hussain, Ayesha Riasat, Salma Kanwal, Mariam Imtiaz, M. O. Ahmad},

journal = {Open Mathematics},

keywords = {Forests; Super edge magic total labeling; Comb; 2-sided generalized comb; Bistar; Deficiency of graph},

language = {eng},

number = {1},

pages = {1431-1439},

title = {Deficiency of forests},

url = {http://eudml.org/doc/288340},

volume = {15},

year = {2017},

}

TY - JOUR

AU - Sana Javed

AU - Mujtaba Hussain

AU - Ayesha Riasat

AU - Salma Kanwal

AU - Mariam Imtiaz

AU - M. O. Ahmad

TI - Deficiency of forests

JO - Open Mathematics

PY - 2017

VL - 15

IS - 1

SP - 1431

EP - 1439

AB - 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].

LA - eng

KW - Forests; Super edge magic total labeling; Comb; 2-sided generalized comb; Bistar; Deficiency of graph

UR - http://eudml.org/doc/288340

ER -

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