Exam 16: Graphs

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A minimum spanning tree of a weighted graph is a spanning tree in which the sum of the weights of the edges is less than or equal to the sum of the weights for any other spanning tree for the same graph.

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A graph is a special kind of tree.

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A(n) _______________________ is one implementation of a graph where the graph is implemented as a linked structure, and each node contains a structure that contains links to all other nodes.

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A graph in which every edge is connected to every other edge is said to be ___________________ .

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Consider the following undirected graph. vertices: 1, 2, 3, 4, 5 edges: (1,2),(3,4), (2,4), (2, 3) Is the graph connected?

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Consider the following undirected graph. vertices: 1, 2, 3, 4, 5 edges: (1,2),(3,4), (2,4), (2, 3) Is the graph acyclic?

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A spanning tree of a graph is a tree with that always has which of the following properties?

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In a(n) _____________________ graph, an edge from node labeled A to a node labeled B is the same as having an edge from B to A.

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A graph with integer weights or costs associated with edges is sometimes called a(n) _________________.

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In an undirected graph, an edge of the form (A, B) is the same as an edge of the form (B, A).

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What does it mean for a graph to be connected?

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What is a complete graph? How many edges are contained in a complete graph on n vertices?

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An undirected graph is connected if for every pair of vertices, there is an edge between them.

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What is the difference between a directed graph and an undirected graph?

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A depth-first traversal of a graph uses which of the following data structures?

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What is the maximum number of edges in a directed graph on n vertices? Explain how you arrived at your solution.

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A digraph is a __________________________ .

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Write out all of the edges in a complete graph on 4 vertices.

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In graph terminology, the nodes are referred to as ____________________.

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A graph is said to have a(n) ________________, if there exists a path where the first and last vertices are the same, and no edge is repeated.

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