Discrete Mathematics - Trees
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The presentation by Marjuk Ahmed Siddiki covers the basics of discrete mathematics and introduces trees as a specific type of undirected graph. Key concepts explained include nodes, edges, root, leaf nodes, depth, height, and relationships such as parent, children, and siblings within tree structures. Furthermore, it discusses various types of trees such as m-ary trees and binary trees.
Discrete Mathematics - Trees
- 2. Hello! I am Marjuk Ahmed Siddiki ID: 171-15-8959 Bio-Informatics Daffodil International University
- 3. Discrete Mathematics - Trees 3
- 4. What is Discrete Math ? "Discrete Math" is not the name of a branch of mathematics, like number theory, algebra, calculus, etc. Rather, it's a description of a set of branches of math that all have in common the feature that they are "discrete" rather than "continuous". Discrete Math What is tree? An undirected graph is a tree if and only if there is a unique simple path between any two of its vertices. Every tree is a Graph, but every Graph is not a tree. 4
- 5. Basic of Tree Node Edge Root Leaf node Depth Height 5 Parent Children Sibling Ancestors Descendants Subtree
- 6. Basic of Tree ○ Node: A node is a fundamental part of a tree. Each letter represents one node. Node often represent entities(complex objects) such as people,car parts etc. ○ Edge: The arrows from one node to another are called edge. Edge betweer the nodes represent the way the nodes are related. 6
- 7. Basic of Tree ○ Root: The root of the tree is the only node in the tree that has no incoming edges. Here, a is the root. 7 ○ Leaf Node: A leaf node is a node that has no children.The bottom nodes (with no outgoing edges) are the leaves . ○ Here, c , i , j , k , l , m are leaves Node.
- 8. Basic of Tree ○ Depth: Depth tells the number of steps (nodes) to get from a node back to the root. 8 ○ Height: The height of a tree is equal to the maximum level of any node in the tree. This tree has height 5, so the maximum depth is 4 (height - 1).
- 9. Basic of Tree Parent: Any node, except root has exactly one edge running upward to another node. The node above it is called parent. a is the parent of b , c , d b is the parent of e d is the parent of f , g , h e is the parent of i , j f is the parent of k h is the parent of l , m 9
- 10. Basic of Tree Sibling: 10 b , c , d are siblings of each other f , g , h are siblings of each other i , j are siblings of each other l , m are siblings of each other
- 11. Basic of Tree Child: Any node may have one or more lines running downward to other nodes. Nodes below are children. 11 b , c , d are children of a f , g , h are children of d e is the children of b i , j are the children of e k is the children of f l , m are the children of h
- 12. Basic of Tree Sub-Tree: A sub-tree of a given node includes one of its children and all of that child's descendants. 12
- 13. Basic of Tree m-ary tree : A rooted tree is called an m-ary tree if every internal vertex has no more than m children. 13 full m-ary tree :A tree is called a full m-ary tree if every internal vertex has exactly m children. m-ary tree full-ary tree
- 14. Basic of Tree binary tree : An m-ary tree with m = 2 is called a binary tree 14
- 15. Thank ❤ YOU