TAILIEUCHUNG - Algorithms and Data Structures in C part 8

The solution to the simple recurrence relation yields, assuming a general form of C(n) = λn followed by a constant to obtain the particular solution | The solution to the simple recurrence relation yields assuming a general form of C n X followed by a constant to obtain the particular solution Applying the boundary condition C 1 1 and C 2 6 one obtains Figure Recursive Model for Boolean Function Evaluation Graphs and Trees This section presents some fundamental definitions and properties of graphs. Definition A graph is a collection of vertices V and associated edges E given by the pair A simple graph is shown in Figure . In the figure the graph shown has Figure A Simple Graph Definition The size of a graph is the number of edges in the graph Definition The order of a graph G is the number of vertices in a graph For the graph in Figure one has Definition The degree of a vertex also referred to as a node in a graph is the number of edges containing the vertex. Definition In a graph G V E two vertices v1 and v2 are neighbors if V1 V2 G E or vj V2 G E In the graph in Figure v1 and v2 are neighbors but v1 and v3 are not neighbors. Definition If G V1 E1 is a graph then H V2 E2 is a subgraph of G written if and . A subgraph of the graph in Figure is shown in Figure . Figure Subgraph of Graph in Figure The subgraph is generated from the original graph by the deletion of a single edge v2 v3 . Definition A path is a collection of neighboring vertices. For the graph in Figure a valid path is Definition A graph is connected if for each vertex pair v vj there is a path from vt to v . The graph in Figure is connected while the graph in Figure is disconnected. Definition A directed graph is a graph with vertices and edges where each edge has a specific direction relative to each of the vertices. An example of a directed graph is shown in Figure . Figure A Directed Graph The graph in the figure has G V E with In a directed graph the edge vi vj is not the same as the edge v vi when i j. The same terminology G V E will be used for .

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