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We study the behaviour of the Igusa-Todorov functions for radical square zeroalgebras. We show that the left and the right $\phi$-dimensions coincide, inthis case. Some general results are given, but we concentrate more in theradical square zero algebras. Our study is based on two notions of hearth andmember of a quiver $Q$. We give some bounds for the $\phi$ and the$\psi$-dimensions and we describe the algebras for which the bound of $\psi$ isobtained. We also exhibit modules for which the $\phi$-dimension is realised.

Igusa-Todorov functions for radical square zero algebras