# Deficiency of forests

Open Mathematics (2017)

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

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## Abstract

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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].

## How to cite

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Sana 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
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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