We introduce an equivalence of plane curve germs which is weaker than Zariski's equisingularity and prove that the set of all Newton diagrams of a germ is an invariant of this equivalence. Then we show how to construct all Newton diagrams of a plane many-branched singularity starting with some invariants of branches and their orders of contact.
Evelia Rosa GARCÍA BARROSO. Andrzej LENARCIK. Arkadiusz PŁOSKI. "Newton diagrams and equivalence of plane curve germs." J. Math. Soc. Japan 59 (1) 81 - 96, January, 2007. https://doi.org/10.2969/jmsj/1180135501