Abstract:
Graphs play an important and vital role in Mathematics. Graph labeling creates
new ideas graph theory. Can labeling be helped us to solve problems in Mathematics
and other fields? The answer of this question increases the deep value of Graph
Labeling. A magic labeling of a graph is described by Kotzig and Rosa [22] in 1970
as an important iniative. A graph labeling (or valuation) is a unique way that gives
the labels to graph elements (commonly, these are non negative or positive integers).
if we consider the domain set of all vertices and edges; such labelings are called
total labelings. Sometime we use labelings for vertex set or the edge set alone and
these labelings would be called as vertex-labeling and edge-labeling respectively. Many
other domains are also possible. There are some famous labelings like as harmonious,
cordial, graceful and antimagic.
In 2000, Baˇca et al. [2] discussed a (a, d)-vertex-antimagic total labeling. A (a, d)-
vertex-antimagic total labeling is called super (a, d)-vertex-antimagic total labeling,
when we give smallest labels to the vertices. An (a, d)-edge-antimagic total labeling
was defined by Simanjuntak et al. [41]. An (a, d)-edge-antimagic total labeling is
called a super (a, d)-edge-antimagic total labeling, when we give the least labels to
the vertices. A graph G, which is made up of cycles with chords is known as Harary
Graph. A brief discussion exposed important results on super (a, d)-edge-antimagic
total labeling Harary graph by M. Baˇca and M. Murugan [1, 6].
This work is designed for the construction of (a, d)-vertex-antimagic total labeling
of Harary graph as well as for super (a, d)-vertex antimagic total labeling of Harary
graph for the different value of d.
