Interlace polynomials of 4n-snowflake graphs

Jyoti Champanerkar (Department of Mathematical Sciences, William Paterson Unviersity, New Jersey, USA)
Aihua Li (Department of Mathematics, Montclair State University, New Jersey, USA)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 11, No 1 (2023): Electronic Journal of Graph Theory and Applications

In this paper, we study the interlace polynomial of a special graph with n vertices, called 4n-snowflake 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.