PPT-Sultan Almuhammadi ICS 254: Graphs and Trees 1 Graph & Trees

Sultan Almuhammadi ICS 254 Graphs and Trees 1 Graph amp Trees Chapters 1011 Acknowledgement This is a modified version of Module22 on Graph Theory by Michael Frank Sultan Almuhammadi ICS 254 Graphs and Trees. Trees are a specific instance of a construct called a graph In general a graph is composed of edges and vertice s that link the nodes together A graph G is often denoted GVE where V is the set of vertices and E the set of edges Two types of graphs Trees and Spanning TreesA graph having no cycles is A graph having no cycles is acyclic.acyclic.A forest is an acyclic graph.is an acyclic graph.A leaf is a vertex of degree 1.is a vertex of degree 1. Applied Discrete Mathematics Week 12: Trees. 1. Representing Graphs. Definition:. Let G = (V, E) be a . directed graph. with |V| = n. Suppose that the vertices of G are listed in arbitrary order as v. Bicoloured. Graphs: Dually Connectedness, . Dual Separators, and Beyond. CAI . Leizhen. The Chinese . Univ. of Hong Kong. Joint work with YE . Junjie. 2. 3. 4. Corneilian. Graph. Charles. Mark. Lorna . Depth First Search (DFS). We Already Covered . Breadth First Search(BFS). Traverses the graph one level at a time. Visit all outgoing edges from a node before you go deeper. Needs a queue. BFS creates a tree called BFS-Tree. Applied Discrete Mathematics Week 14: Trees. 1. Representing Graphs. Definition:. Let G = (V, E) be a . directed graph. with |V| = n. Suppose that the vertices of G are listed in arbitrary order as v. Graph Isomorphism. 2. Today. Graph isomorphism: definition. Complexity: isomorphism completeness. The refinement heuristic. Isomorphism for trees. Rooted trees. Unrooted trees. Graph Isomorphism. 3. Graph Isomorphism. Introduction to Trees. Applications of Trees. (. not currently included in overheads. ). Tree Traversal. Spanning Trees. Minimum Spanning Trees (. not currently included in overheads. ). Introduction to Trees. A . tree. is a connected undirected graph with no simple circuits.. Since a tree cannot have a simple circuit, a tree cannot contain multiple edges or loops.. Therefore, any tree must be a . simple graph. Quarter: Summer 2017. CSE 373: Data Structures and Algorithms. Lecture . 14: Introduction to Graphs. Today. Overview of Midterm. Introduce Graphs. Mathematical representation. Undirected & Directed Graphs. Dr. Halimah Alshehri. 1. Introduction to Trees. DEFINITION 1 . A . tree. is a connected undirected graph with no simple circuits.. Because . a tree cannot have a simple circuit. , . a tree cannot contain multiple edges or loops. Fall. 2017. Sukumar Ghosh. Seven Bridges of . K. ⍥. nigsberg. Is it possible to walk along a route that cross . each bridge exactly once?. Seven Bridges of . K. ⍥. nigsberg. A Graph. What is a Graph. AVL Trees 1 AVL Trees 6 3 8 4 v z AVL Trees 2 AVL Tree Definition Adelson- Velsky and Landis binary search tree balanced each internal node v the heights of the children of v can differ by at most 1 www.aaaai.org OAAC 522 v2017