Definition of "preorder"

Example 436 For each set A {\displaystyle A} , the relation ⊆ {\displaystyle \subseteq } is a preorder on P ( A ) {\displaystyle {\mathcal {P}}(A)} .

2002, Yves Nievergelt, Foundations of Logic and Mathematics‎, Springer (Birkhäuser), page 152

Let us first compare S 1 {\displaystyle S_{1}} , S 2 {\displaystyle S_{2}} and S 3 {\displaystyle S_{3}} w.r.t. the partial preorder ⪰ {\displaystyle \succeq } .

2010, S. Kaci, “Refined Preference-Based Argumentation Frameworks”, in Pietro Baroni, F. Cerutti, M. Giacomin, G. R. Simari, editors, Computational Models of Argument: Proceedings of COMMA 2010, IOS Press, page 306

It can easily be verified that the above relation is a preorder, i.e. that it is reflexive and transitive.

2000, Jean-Charles Pomerol, Sergio Barba-Romero, Multicriterion Decision in Management: Principles and Practice, Springer, Softcover, page 58

Now, the preorder traversal of a tree can be constructed from the preorder traversals of the subtrees rooted at the children of the root of the tree.

2002, Gabriel Valiente, Algorithms on Trees and Graphs, Springer, page 115

In the program given above, tree is constructed and is traversed in inorder, preorder and postorder traversal.

2006, ISRD Group, Data Structures Using C, Tata McGraw-Hill Education, page 254

The preorder traversal visits a node first after which it traverses its left subtree and then traverses its right subtree.

2011, Ananda Rao Akepogu, Radhika Raju Palagiri, Data Structures and Algorithms Using C++, Pearson Education India, page 9.16