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    Hosoya Polynomial of Graphs Belonging to Twist Knots
    (2018) 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.
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    On Domination Polynomials of Caterpillar Graphs
    (2018) Şahin, Bünyamin; Şahin, Abdulgani
    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.
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    Tutte Polynomial for Graphs of Twist Knots
    (2018) 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.