Question 1 And Question 2 - Point And Note It Is Recommended

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Question 1 (1 point) Question 2 (1 point) Note: It is recommended that you save your response as you complete each question. Subsection For the rooted tree shown below, match the description on the left with the correct list of vertices. a, c, g, l, n m, n, p, q, r n e, f, h, k, o, p, q, r b, c, d, g, i, l, m, n 1. Siblings of m 2. Descendants of l 3. Leaves 4. Internal vertices 5. Ancestors of r Save Determine the order in which an inorder traversal visits the vertices of the rooted tree shown below. Question 3 (1 point) Question 4 (1 point) i, k, d, e, b, m, n, l, g, h, c, a m, n, i, k, l, d, e, g, h, b, c, a i, d, k, b, e, a, m, l, n, g, c, h i, d, b, a, h, m, l, g, c, n , h Save Which one of the following statements is false? A full binary tree has an even number of vertices. A binary tree is an m-ary with m = 2. In an m-ary tree, each internal vertex has at most m children. In a full m-ary tree, each internal vertex has exactly m children. Save Determine the order in which a preorder traversal visits the vertices of the rooted tree shown below. Question 5 (1 point) Question 6 (1 point) a, b, d, i, k, e, c, g, l, m, n, h a, b, c, d, e, g, h, i, k, l, m, n a, b, d, e, i, k, c, g, h, l, m, n a, b, d, i, e, k, c, g, m, l, n, h Save How many edges must be removed from the wheel graph W6 in order to create a spanning tree for the graph? The graph does not have a spanning tree. Save Which of the graphs are trees? H1 and H4 only H2 and H3 only H2 and H5 only H1, H3, and H4 only H2, H4, and H5 only Save Save All Responses Go To Submit Quiz

Paper For Above instruction

The set of questions provided encompasses various fundamental topics in graph theory and tree data structures, including traversal methods, properties of specific types of graphs and trees, and concepts related to connectivity and spanning trees. This paper aims to systematically analyze these topics, elucidating their theoretical foundations, practical implications, and computational aspects, while applying them to the specific scenarios delineated in the exam questions.

Introduction to Tree and Graph Structures

Trees and graphs are essential constructs in computer science, underpinning numerous algorithms and data structures. A rooted tree is a hierarchical structure with a designated root node, from which all other nodes descend through parent-child relationships. Traversal techniques such as inorder, preorder, and postorder are systematic methods for visiting all nodes in a tree, each producing a unique node visitation sequence crucial for various applications like expression evaluation, syntax parsing, and hierarchical data representation.

Tree Traversal Methods and Their Significance

Inorder traversal involves visiting the left subtree, then the node itself, followed by the right subtree. This sequence is particularly significant in binary search trees, where it results in visiting nodes in ascending order. Preorder traversal visits the node first, then recursively traverses the left and right subtrees, which is useful in scenarios such as copying trees or generating prefix expressions. Postorder traversal visits all subtrees prior to the node itself, suitable for deleting trees or generating postfix expressions.

Analyzing Specific Questions and Their Conceptual Basis

Question 2 requires matching descriptors like siblings, descendants, leaves, internal nodes, and ancestors with specific sets of vertices in a rooted tree. Such questions probe understanding of hierarchical structures and the relationships within trees. For example, siblings are nodes sharing the same parent, descendants are nodes reachable from a given node, and ancestors are nodes along the path to the root.

Question 3 asks for inorder traversal order of a specific rooted tree. The sequence reflects the recursive visiting pattern, which can be verified by systematically following the inorder process node-by-node.

Question 4 presents statements about binary and m-ary trees, asking for identification of the false statement. Recognizing properties such as the number of vertices in full binary trees and the maximum number of children per internal node is fundamental in classifying tree types and understanding their constraints.

Preorder Traversal and Its Application

Question 5 tests comprehension of preorder traversal sequence. Understanding the order in which nodes are visited—starting at the root and proceeding through each subtree—helps in tasks like tree duplication and expression tree evaluation.

Graph Connectivity and Spanning Trees

Question 6 pertains to spanning trees, a core concept in graph theory relating to the minimum set of edges that connect all vertices without cycles. For a wheel graph W6, which combines a cycle with a central hub, removing edges to form a spanning tree involves eliminating enough edges to break cycles while maintaining connectivity. Since a wheel graph with 6 vertices has 12 edges, a spanning tree must have 5 edges, meaning 7 edges need to be removed.

Identifying Trees Among Graphs

Questions about whether certain graphs are trees require analyzing their structure for cycles and connectivity. A tree has no cycles and is connected. Recognizing such features in specific graphs (H1 through H5) involves examining their edges and verifying the absence of cycles combined with connectivity criteria.

Conclusion

In summary, mastery of tree traversal techniques, understanding of hierarchical relationships, properties distinguishing different classes of trees, and the ability to analyze graph properties are vital skills in computer science. These concepts not only underpin theoretical understanding but also have practical applications in areas like database indexing, network design, and compiler construction. The questions examined highlight the importance of these foundational topics, emphasizing their relevance across various computational contexts.

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