Database System Concepts
7th Edition
ISBN: 9780078022159
Author: Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher: McGraw-Hill Education
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Show that every nonincreasing sequence of nonnegative integers with an even sum of its terms is the degree sequence of a pseudograph, that is, an undirected graph where loops are allowed. [Hint: Construct such a graph by first adding as many loops as possible at each vertex. Then add additional edges connecting vertices of odd degree. Explain why this construction works.]
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- Suppose we have a graph as follows A) Show the order of visit for the vertices using Depth First Traversal. B) Show the order of visit for the vertices using Breadth First Traversal. PLEASE HELP WITH PARTS A AND B WITH WORKarrow_forwardConstruct a simple graph with vertices A,B,C,D,E,F whose degrees are 3, 1, 1, 2, 3, 2. (For example, a simple graph with vertices a,b,c whose degrees are 1,2,1 has edge set {{a,b},{b,c}}.) What is the edge set?arrow_forwardLet n be an even positive integer. (a) Show that if the degree of every vertex in a simple graph G on n vertices is at least (i.e., greater than or equal to) n/2, then G must be connected. (b) Give an example of a disconnected simple graph on n vertices in which every vertex has degree (n/2) – 1.arrow_forward
- B Write a topological order of vertices of above graph and illustrate your method.arrow_forwardGive, with justification, a formula for the minimum number of edges that must be added to a general connected graph to make it have an Euler tour, provided we allow multiple edges (that is, two vertices can be joined by more than one edge).arrow_forwardWhat is the minimum number of 1’s in the adjacency matrix of a connected undirected graph of N vertices (without self–loops) ? How many 1’s are in the adjacency matrix of a complete graph of N vertices?arrow_forward
- Let G be a graph with n vertices. If the maximum size of an independent set in G is k, clearly explain why the minimum size of a vertex cover in G is n - k.arrow_forwardYou are given a simple graph. Prove that there must be at least two vertices with the same degree.arrow_forwardShow a simple disconnected graph with 6 vertices and 2 connected components.arrow_forward
- Please solve with the computer Question 2: Draw a simple undirected graph G that has 11 vertices, 7 edges.arrow_forwardConsider an undirected graph G with 100 nodes. The maximum number of edges to be included in G so that the graph is not connected isarrow_forwardIs there a connected planar graph with an odd number of faces where every vertex has degree 6? Prove your answer.arrow_forward
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