data structures using according to the first propertythe root of heap-ordered tree contains the smallest key in the tree the second propertyon the other handimplies that binomial heap having nodes contains at most log ( binomial trees linked representation of binomial heaps each node in binomial heap has val field that stores its value in additioneach node has following pointersp[nthat points to the parent of child[nthat points to the leftmost child sibling[nthat points to the sibling of which is immediately to its right if is the root nodethen [nnull if has no childrenthen head [ child[nnulland if is the rightmost child of its parentthen sibling[nnil in addition to thisevery node has degree field which stores the number of children of look at the binomial heap shown in fig figure shows its corresponding linked representation figure binomial heap parent null null null child head [hvalue degree sibling null null null null null null null null null null null null figure linked representation of the binomial tree shown in fig operations on binomial heaps in this sectionwe will discuss the different operations that can be performed on binomial heaps creating new binomial heap the procedure create_binomial-heap(allocates and returns an object hwhere head[his set to null the running time of this procedure can be given as ( finding the node with minimum key the procedure min_binomial-heap(returns pointer to the node which has the minimum value in the binomial heap the algorithm for min_binomial-heap(is shown in fig