Interlace polynomials of 4n-snowflake graphs

In this paper, we study the interlace polynomial of a special graph with n vertices, called 4nsnowflake graph. It is similar as the friendship graph Fn of n vertices, which is made of n 3-cycles sharing one center vertex. In stead of 3-cycles, the 4n-snowflake graph Qn is constructed by gluing n 4-cycles to one center vertex. We describe certain properties of such graphs, provide recursive and explicit formulas for the interlace polynomials, and give some properties of such polynomials such as special values and patterns for certain coefficients.