Equivalence Of Super Magic Labelings

Selvam Avadayappan; S. Kalaimathy; P. Mahalakshmi

doi:https://doi.org/10.14445/22315373/IJMTT-V4I3P502

International Journal of Mathematics Trends and Technology

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Volume 4 | Issue 3 | Year 2013 | Article Id. IJMTT-V4I3P502 | DOI : https://doi.org/10.14445/22315373/IJMTT-V4I3P502

Equivalence Of Super Magic Labelings

Selvam Avadayappan, S. Kalaimathy, P. Mahalakshmi

Abstract

Let G (V, E) be a graph with p vertices and q edges. A bijection f : V E  {1,2,…., p+q} is called a super magic labeling of a graph G, if f(V) = {1, 2,…., p} and for any edge xyE, f(x)+f(y)+f(xy) = c(f), a constant. The super magic strength of a graph G, sm(G) is defined as the minimum of all c(f) where the minimum runs over all super magic labelings f of G. Recently a new version of super magic labeling has been introduced. For the graph G(V, E), a bijection f : V E  {1, 2,…., p+q} is called a super magic (special) labeling of G, if f(E) = {1, 2,…., q} for any edge xyE such that f(x)+f(y)+f(xy) = c'(f), a constant. The super magic (special) strength of a graph G, sms(G) is defined as the minimum of all c'(f) where the minimum is taken over all super magic special labelings f of G. In this paper, we prove that sms(G) = 2q-p+sm(G).

Keywords

Graph labeling, Magic labeling, Magic strength, Super magic labeling, Super magic strength.

References

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Citation :

Selvam Avadayappan, S. Kalaimathy, P. Mahalakshmi, "Equivalence Of Super Magic Labelings," International Journal of Mathematics Trends and Technology (IJMTT), vol. 4, no. 3, pp. 53-57, 2013. Crossref, https://doi.org/10.14445/22315373/IJMTT-V4I3P502