An edge-magic total labeling of an .n; m/-graph G D .V; E/ is a one to one map from V .G/ [ E.G/ onto the integers f1; 2; : : : ; n C mg with the property that there exists an integer constant c such that .x/ C .y/ C .xy/ D c for any xy 2 E.G/. It is called super edge-magic total labeling if .V .G// D f1; 2; : : : ; ng. Furthermore, if G has no super edge-magic total labeling, then the minimum number of vertices added to G to have a super edgemagic total labeling, called super edge-magic deficiency of a graph G, is denoted by s .G/ [4]. If such vertices do not exist, then deficiency of G will be C1. 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 .
A super edge-magic total (SEMT) labeling of a graph ℘(V, E) is a one-one map ϒ from V(℘)∪E(℘) onto {1, 2,…,|V (℘)∪E(℘) |} such that ∃ a constant “a” satisfying ϒ(υ) + ϒ(υν) + ϒ(ν) = a, for each edge υν ∈E(℘), moreover all vertices must receive the smallest labels. The super edge-magic total (SEMT) strength, sm(℘), of a graph ℘ is the minimum of all magic constants a(ϒ), where the minimum runs over all the SEMT labelings of ℘. This minimum is defined only if the graph has at least one such SEMT labeling. Furthermore, the super edge-magic total (SEMT) deficiency for a graph ℘, signified as $\mu_{s}(\wp)$ is the least non-negative integer n so that ℘∪nK1 has a SEMT labeling or +∞ if such n does not exist. In this paper, we will formulate the results on SEMT labeling and deficiency of fork, H -tree and disjoint union of fork with star, bistar and path. Moreover, we will evaluate the SEMT strength for trees.
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