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Deficiency of forests

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Javed S., Hussain M., Riasat A., Kanwal S., Imtiaz M., Ahmad M. O.

Open Mathematics

2017

tom 15

nr 1

1431-1439

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].

Ograniczanie wyników

1 Open Mathematics

1 Ahmad M. O.

1 Hussain M.

1 Imtiaz M.

1 Javed S.

1 Kanwal S.

1 Riasat A.

1 2017

Wyniki wyszukiwania

Deficiency of forests