Data structure graphs

Data structure graphs

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  DATA STRUCTURE -GRAPHS Dr.M.UMADEVI ASSISTANTPROFESSOR DEPARTMENT OF CS SACWC CUMBUM
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  Introduction to Graphs Graph is a non linear data structure; A map is a well-known example of a graph.  In a map various connections are made between the cities. The cities are connected via roads, railway lines and aerial network.  We can assume that the graph is the interconnection of cities by roads. Euler used graph theory to solve Seven Bridges of Königsberg problem.
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  Defining the degreeof a vertex to be the number of edges incident to it, Euler showed that there is a walk starting at any vertex, going through each edge exactly once and terminating at the start vertex iff the degree of each, vertex is even. A walk which does this is called Eulerian. There is no Eulerian walk for the Koenigsberg bridge problem as all four vertices are of odd degree. A graph contains a set of points known as nodes (or vertices) and set of links known as edges (or Arcs) which connects the vertices. A
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  A graph isdefined as Graph is a collection of vertices and arcs which connects vertices in the graph. A graph G is represented as G = ( V , E ), where V is set of vertices and E is set of edges. Example: graph G can be defined as G = ( V , E ) Where V = {A,B,C,D,E} and E = {(A,B),(A,C)(A,D),(B,D),(C,D),(B,E),(E,D)}. This is a graph with 5 vertices and 6 edges
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  Graph Terminology 1.Vertex :An individual data element of a graph is called as Vertex. Vertex is also known as node. In above example graph, A, B, C, D & E are known as vertices. 2.Edge : An edge is a connecting link between two vertices. Edge is also known as Arc. An edge is represented as (starting Vertex, ending Vertex). In above graph, the link between vertices A and B is represented as (A,B). Edges are three types: 1.Undirected Edge - An undirected edge is a bidirectional edge. If there is an undirected edge between vertices A and B then edge (A , B) is equal to edge (B , A). 2.Directed Edge - A directed edge is a unidirectional edge. If there is a directed edge between vertices A and B then edge (A , B) is not equal to edge (B , A
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