Interlace Polynomials of $n$-Claw Graphs

Abstract

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.