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notes124 - A graph G=(V,E is composed of V set of vertices...

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A graph G=(V,E) is composed of V: set of vertices E: set of edges An edge e=(V,V) is a pair of vertices V={A,B,C,D,E} E={(A,B),(A,D),(A,C),(B,E),(C,D),(C,E)} Graphs are useful to model a lot of real life problems -communication network -transport network :streets, intersections etc -electronic circuits -event dependencies
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GRAPH TERMINOLOGY a. Adjacent vertices : vertices connected by an edge B,C,D are adjacent to A b. Degree of a matrix : number of adjacent vertices Degree of A is 3 Degree (V)=2(number of edges) Degree (A)=3 Degree (B)=2 Degree (C)=2 Degree (D)=1 ------------ 8 = 2(4) Path is a sequence of vertices V 1 ,V 2 ….V k such that consecutive vertices Vi and Vi+1 are adjacent. A, B, C, D is a path A, B, D is not a path Simple path is a path with no repeated vertices. A cycle is similar to a simple path except that the first vertex is the same as the last vertex. Ex: A,B,C,A.
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Connected graph is a graph where any two vertices are connected by the same path. Subgraph is a subset of vertices and edges of a graph Connected components : the maximal connected graphs of an original graph.
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This graph has 3 connected components. Tree i s a connected graph without cycles. Forest
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This note was uploaded on 02/02/2012 for the course CS 251 taught by Professor Staff during the Fall '08 term at Purdue.

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notes124 - A graph G=(V,E is composed of V set of vertices...

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