Equivalence Of Super Magic Labelings
Journal Title: INTERNATIONAL JOURNAL OF MATHEMATICS TRENDS AND TECHNOLOGY - Year 2013, Vol 4, Issue 3
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 xyE, 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 xyE 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).
Authors and Affiliations
Selvam Avadayappan, S. Kalaimathy, P. Mahalakshmi
Keywords
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