# gt - Graphs, Traversal Algorithms Contents Introduction...

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Graphs, Traversal Algorithms Contents Introduction Walks, Paths, and Circuits Shortest Path Algorithms Problems Introduction Graph theory is used in many diverse fields including: chemistry electrical engineering operations research linguistics economics mathematics computer science Computer scientists use graphs to model: networks circuit layout numerical analysis We can use it as a general problem solving tool. For example, find the shortest path between 2 cities in a transportation network. Definitions A graph G is composed of a finite set of vertices and a finite set of edges. A graph is denoted G(V,E) An edge is associated with a set consisting of either 1 or 2 vertices (endpoints) An edge associated with one vertex is called a loop. Two distinct edges with the same endpoints are called parallel edges.

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Two vertices that are connected by an edge are called adjacent. An edge is called incident on each of its endpoints. Two edges incident on the same endpoints are called adjacent. A vertex with no edges incident on it is isolated. A graph with no vertices is empty. Directed Graph In graph theory, we can describe the digraph G as a finite set of vertices and a finite set of directed edges, where each edge is associated with an ordered pair of vertices called its endpoints. Example: Directed Graph Not A Directed Graph Simple Graph A simple graph G is a graph that doesn’t have loops or parallel edges. Example: Simple Graph Not A Simple Graph
A complete graph on n vertices, k n , is a simple graph with n vertices v 1 , v 2 , ...v n whose set of edges contain exactly one edge for every pair of distinct vertices. Example: Complete Graph Not A Complete Graph Bipartite Graph A graph G is bipartite if V= (V1 union V2) and V1 and V2 are disjoint, and every edge is of the form {a,b} where a is an element of V1 and b is an element of V2. Complete Bipartite Graph A complete bipartite graph is a bipartite graph such that every vertex in V1 is joined with every vertex in V2. Example

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## gt - Graphs, Traversal Algorithms Contents Introduction...

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