Alkan, Akın; Kocayiğit, Hüseyin; Ağırman Aydın, Tuba

In this study, we consider Di-Darboux slant helices which are new surface curves on an oriented surface. We give some characterizations for such curves according to the Darboux frame, OD-frame, ND-frame, RD-frame, and obtain axes of the Di-Darboux slant helices. Moreover, the position vectors of the Di-Darboux slant helices are obtained.

AtıfOpenAlex2

İncele

Aydın, Tuba Ağırman; Kocayiğit, Hüseyin; Kara, Meryem

In this paper, we obtain some characterizations for a Frenet curve with the help of an alternative frame different from the Frenet frame. Also, in the present study, we consider weak biharmonic and harmonic 1-type curves by using the mean curvature vector field of the curve. We also study 1-type and biharmonic curves whose mean curvature vector field is in the kernel of Laplacian. We give some theorems for such curves in the Euclidean 3-space. Moreover, we give the classifications of these types of curves.

İncele

Aydın, Tuba Ağırman; Kocayigit, Hüseyin

In this study, a kind of generalized involute and evolute curve pair is considered in 4 dimensional semi Euclidean space with 2 index. The curvatures and the associated Frenet Frame of this kind of generalized involute-evolute curve pair are presented.

AtıfOpenAlex1

İncele

Şahin, Abdulgani; Şahin, Bünyamin

The domination polynomial of a simple graph G is calculated with D(G, x) =Pn i=1 d(G, i)x i such thatd(G, i) is the number of the dominating sets of G of size i. In this paper we study the domination polynomials ofcaterpillar graphs.

İncele

Şahin, Abdulgani; Şahin, Bünyamin

There is a deep relationship between knot theory and graph theory. Graphs are effective tools forstudies into knot theory. It is possible to switch between the two theories by forming the graphs of knots. Thus, thestudy areas of the two theories meet on a common ground. In this study, we firstly introduce Hosoya polynomialand we work out the Hosoya polynomials for graphs of twist knots which are one of interesting families of knotsand try to get a generalization for them.

İncele

Şahin, Abdulgani; Şahin, Bünyamin

The Tutte polynomial is a two-variable polynomial that is connected by a graph, a matroid or a matrix.The Tutte polynomial has a lot of exciting applications in different areas for example combinatorics, probability,knot theory, algebra, statistical mechanics, computer sciences, chemistry and biology. It was indicated by W. T.Tutte. We transport the Tutte polynomial to knot theory. Because each knot have a corresponding graph. Westudy the Tutte polynomial for graphs of twist knots. We find some general forms for the Tutte polynomial ofgraphs belonging to twist knots and the Tutte polynomial of signed graphs belonging to twist knots. Twist knotsare significant class of knots to take into account especially in contact geometry.

İncele