Word Count : 598

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A tree is a connected graph that contains no cycles. It is one of the most important structures in Data Structures and Algorithms because it provides an efficient way to represent hierarchical relationships. A bipartite graph is a graph whose set of vertices can be divided into two disjoint sets such that every edge connects a vertex from one set to the other. There are no edges between vertices belonging to the same set. To show that every tree is a bipartite graph, it is necessary to prove that such a partition always exists for any tree. One of the simplest ways to prove this property is by using the concept of levels in a tree. Select any vertex of the tree as the root. Starting from the root, assign level 0 to it. All vertices directly connected to the root are assigned level 1. Their children are assigned ________ _____ _______ _____ _____ __________ ______ ___ ___ _______ ___.
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