Abstract
In this paper, we study the interlace polynomial of a special graph with n vertices, called 4 n -snowflake graph. It is similar as the friendship graph F n of n vertices, which is made of n 3-cycles sharing one center vertex. In stead of 3-cycles, the 4 n -snowflake graph Q n 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.
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