Hosoya Polynomial of Graphs Belonging to Twist Knots

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.