This is the recipe theorem of Tutte polynomial and I have one confusion regarding this. As mentioned in the title, What does this asterisk symbol means here in this definition. Is this the cartesian product or disjoint union?
2026-02-24 03:33:04.1771903984
What does the "$*$" in "$G_1*G_2$" mean for graphs (as part of the recipe theorem for the Tutte polynomial)?
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It is a one-point join of $G_1$ and $G_2$. See page 5 of Graph Polynomials and Their Applications I: The Tutte Polynomial, by Joanna A. Ellis-Monaghan and Criel Merino. Definition 5 on page 7 looks just like your Definition 4.1.