Types of Graphs in Computer Engineering: Visualization for Data and Algorithms

Types of Graphs in Computer Engineering: Visualization for Data and Algorithms

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  Types of Graphs
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  Team Amit Golder ID: 201-15-3058 MarcelDavid Baroi ID: 201-15-3421 MD: Mehedy Hasan Monir ID: 201-15-3508 Tanvir Niaz Khan ID: 201-15-3593
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  Topics Graph Directed Undirected Adjacent Vertices The Degree of aVertex Isolated and Pendant Vertices Adjacent Vertex In-Degree and Out- Degree Complete Graph Cycle Wheels The n-Dimensional Hypercube Subgraph Union of Graphs Regular Graph Type of Graph Simple Graph Multiraph
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  Adjacent Vertices 2 3 2 3 2 1 Two verticesu and v in an undirected graph G are called adjacent (or neighbors) in G if u and v are endpoints of an edge of G. u v
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  The degree ofa vertex in an undirected graph is the number of edges incident with it, except that a loop at a vertex contributes twice to the degree of a vertex 2 4 2 3 5 1 maximum degree = 5 minimum degree = 1 The Degree of a Vertex
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  Isolated and PendantVertices 2 4 2 3 5 1 0 A vertex of degree zero is called isolated. It follows that an isolated vertex is not adjacent to any vertex. A vertex is pendant if and only if it has a degree one. Consequently, a pendant vertex is adjacent to exactly one other vertex
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  Adjacent Vertex a d ef b c When (u, v) is an edge of the graph G with directed edges, u is said to be adjacent to v and v is said to be adjacent from u The vertex u is called initial vertex of (u, v) and v is called the terminal or end vertex of (u, v). u v
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  In-Degree and Out-Degree a de f b c In a graph with directed edges the in-degree of a vertex a, denoted by deg−(a), is the number of edges with v as their terminal vertex. deg−(a) = 2 The out-degree of a, denoted by deg+(a), is the number of edges with v as their initial vertex. deg+(a) = 4
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  The complete graphon n vertices, denoted by Kn, is the simple graph that contains exactly one edge between each pair of distinct vertices. Complete Graph The graphs Kn for 1 ≤ n ≤ 6
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  Cycle The cycle Cn,n ≥ 3, consists of n vertices v1, v2, ..., vn and edges {v1, v2}, {v2, v3}, ..., {vn−1, vn} and {vn, v1}. The graphs Cn , 3 ≤ n ≤ 6
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  Wheels The graphs Wnfor 3 ≤ n ≤ 6 We obtain the wheel Wn when we add an additional vertex to the cycle Cn for n ≥ 3 and connect this new vertex to each of the n vertices in Cn, by new edges
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  The n-Dimensional Hypercube Then-dimensional hypercube, or n-cube, denoted by Qn, is the graph that has vertices representing the 2n bit strings of length n. Two vertices are adjacent if and only if the bit strings that they represent differ in exactly one bit position. The graphs Qn for 1 ≤ n ≤ 3
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  Sub-graph G H A subgraphof a graph G = (V, E) is a graph H = (W , F) where W V and F E. ⊆ ⊆
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  Union of Graphs Theunion of two simple graphs G1 = (V1, E1) and G2 = (V2, E2) is the simple graph with vertex set V1 V2 and edge set E1 E2. The union of G1 and G2 is denoted by G1 G2. ∪ ∪ ∪ G1 G2 ∪ G2 G1
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  Regular Graph A simplegraph is called regular if every vertex of this graph has the same degree. A regular graph is called n-regular if every vertex in this graph has degree n.
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  Simple Graph A simplegraph is the undirected graph with no parallel edges and no loops. A simple graph which has n vertices, the degree of every vertex is at most n -1.
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  Multiraph A multigraph isdifferent from a hypergraph, which is a graph in which an edge can connect any number of nodes, not just two
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  Thank You