Abstract
Let C = (M, N) be a finite, undirected and simple
graph with |M(C)| = t and |N(C)| = s. The labeling of a
particular graph is a function which maps vertices and edges of
graph or both into numbers (generally +ve integers).
If the domain of the given graph is the vertex-set then the
labeling is described as a vertex labeling and if the domain of
the given graph is the edge-set then the labeling is defined as an
edge labeling. If the domain of the graph is the set of vertices
and edges then the labeling defined as a total labeling.
A graph will be termed as magic, if there is an edge labeling,
using the positive numbers, in such a way that the sums of the
edge labels in the order of a vertex equals a constant (generallycalled an index of labeling), without considering the choice of
the vertex.
An edge magic total labeling of a given graph comprising t
vertices and s edges is a (1 − 1) function that maps the vertices
and edges onto the integers 1, 2, . . . , t+s, with the intention that
the sums of the labels on the edges and the labels of their end
vertices are always an identical number, consequently they are
independent of any specific edge. To a greater extent, we can
define a labeling as super if the t least possible labels happen at
the vertices.
The Super edge-magic deficiency of a graph C, signified as
µs(C), is the least non negative integer m0
so that C ∪m0K1 has
a Super edge-magic total labeling or +∞ if such m0 does not
exist.
In this paper, we will take a look at the Super edge-magic
deficiencies of acyclic graphs for instance disjoint union of shrub
graph with star, disjoint union of the shrub graph with two stars
and disjoint union of the shrub graph with path.
Aasma Khalid. A, Gul Sana, Maryem Khidmat, A.Q.Baig. (2015) Super Edge-Magic Deficiency of Disjoint Union of Shrub Tree, Star and Path Graphs, Punjab University Journal of Mathematics, Volume 47, Issue 2.
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