Interlace Polynomials of \(n\)-Claw Graphs

In this paper, we present the study of the interlace polynomials for \( n \)-claw graphs. For a positive integer \( n > 1 \), an \( n \)-claw graph \( W_n \) is a tree that has one center vertex and \( n \) claws. The center vertex is connected to one vertex of each of the \( n \) claws using one edge of the claw. We present iterative formulas and explicit formulas for the interlace polynomial of \( W_n \). Furthermore, some interesting properties of the polynomial are discussed.