الفهرس 
Preliminaries of Knot Theory
The Unknotting NumberOnly 14 pages are availabe for public view
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Abstract
The main purpose of this thesis is to obtain some new cri-
teria of periodicity of links depending on some polynomial
link invariants. Speci cally, we try to have some progress
toward solving a well-known conjecture in knot theory that
the period of a periodic alternating link divides its crossing
number.
In Chapter 1: We give a historical introduction of knot
theory along the time together with an overview of the main
concepts and de nitions. Also, we recall some of classical
link invariants and the Reidemeister moves that we use many
times in our work.
In Chapter 2: We study some polynomial invariants in one
variable as the Kauman bracket and the Jones polynomial.
We study dierent approaches of the Jones polynomial. We
evaluate the Jones polynomial of some links by hand. We
end this chapter by making an evaluation for the Jones poly-
nomial to feel the need to other types of polynomial link
invariants.
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In Chapter 3: We study some polynomial link invariants
in more than one variable such as the Hom y polynomial
and the Kauman polynomial. We compute these polyno-
mials for some links. Also, we put a separate section to give
some pieces of advice and some important notes to avoid
some common mistakes in hand computations of Kauman
polynomial.
In Chapter 4: We study the Hom y polynomial of the
knotted trivalent plane graphs and we show that the Hom-
y polynomial of a periodic knotted trivalent graph satis es
some special form. Therefore, the periodicity of the knotted
trivalent plane graphs is re ected in this polynomial. The
main results in this chapter is published in Asian Research
Journal of Mathematics, 7(2): 1-7, 2017; Article no. AR-
JOM. 37847.
In Chapter 5: We study a Kauman polynomial in three
variables that de ned on the knotted trivalent graphs and
some criteria of their periodicity. from this, we derive cri-
teria for periodicity of links especially for adequate links.
Moreover, this gives some progress toward positive solution
of the conjecture that the period divides the crossing num-
ber of the adequate link. This may help in solving the main
conjecture of the periodic alternating links. The main re-
sults in this chapter is published in Bulletin of the Korean
Mathematical Society, 55(2018), no. 3, pp. 799-808.