b) Give an example of each of the following: A graph G with x(G) > @(G) = 3 A graph G which is 4-critical. i) ii) Let T be a tree with at least 3 vertices. Let T' be the graph obtained from T by deleting all the leaves. Show that c) i) T' is a tree, ii) T and T' have the same centre. d) Find the diameter and radius of the following graph.

b) Give an example of each of the following: A graph G with x(G) > @(G) = 3 A graph G which is 4-critical. i) ii) Let T be a tree with at least 3 vertices. Let T' be the graph obtained from T by deleting all the leaves. Show that c) i) T' is a tree, ii) T and T' have the same centre. d) Find the diameter and radius of the following graph.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Graph Theory Question 9.6 Graph G is an n-vertex graph. For integer n ≥ 3, let every new graph formed by deleting a vertex from G be a tree. Answer the following two questions: 1. What is the number of edges of G 2. Prove why G is a cycle of Cn on n vertices
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1) There is undirected graph below. Please give traversal results of BFS and DFS respectively, assuming start from vertex G.< Undirected ↓ G A D B C F E
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Q2 a Let G be a graph. We say that a set of vertices C form a vertex cover if every edge of G is incident to at least one vertex in C. We say that a set of vertices I form an independent set if no edge in G connects two vertices from I. For example, if G is the graph above, C = [b, d, e, f, g, h, j] is a vertex cover since each of the 20 edges in the graph has at least one endpoint in C, and I = [a, c, i, k] is an independent set because none of these edges appear in the graph: ac, ai, ak, ci, ck, ik. In the example above, notice that each vertex belongs to the vertex cover C or the independent set I. Do you think that this is a coincidence? In the above graph, clearly explain why the maximum size of an independent set is 5. In other words, carefully explain why there does not exist an independent set with 6 or more vertices.
1) Consider the following Graph. 2 3 4. 5 write D, A, and L Matrix of the above graph Draw one spanning Tree For above graph