I think your question is if I have a tree methods to price American option , can I use or modify it to European option.

To that question, the answer is yes and simple. American options need one more step than European one to calculate value at the nodes of exercise:

Max(intrinsic value, discount value from next (time) level nodes )

If you remove these Max (…, …) from American tree  except maturity nodes which only have intrinsic value, then you get the European  tree. Ie just use discount value from next level notes as the value at that node for European options.

Or  if not, It may be interesting to know what your acadmeic research is about. I am not sure if any quants would go crasy to do N dimensional  M-nomial trees.

binomial tree是可以用来评价欧式的，美式的只是在欧式的基础上多了一步：置换内在价值（欧式价格）和提前执行价值。

我猜你的意思是想建立2个独立的二叉树，然后比较各个时间点上的时间价值，看是否可以进行套利？

我记得有本书是有matlab code的，现在出了第二版，貌似是什么matlab in finance and economic，第一版是什么matlab in finance。Google一下吧