Fibonacci Heap - Decrease Key and Delete Operations
Operation decrease key will take the node, decrease the key and if the heap property becomes violated (the new key is smaller than the key of the parent), the node is cut from its parent. If the parent is not a root, it is marked. If it has been marked already, it is cut as well and its parent is marked. We continue upwards until we reach either the root or an unmarked node
Ref: https://en.wikipedia.org/wiki/Fibonac...
Introduction to Algorithms by CLRS
some internet sources