Could you Please Choose the correct answer without explanation ..Thank you Are these two graphs isomorphic? Why?O None of them.These graphs are not isomorphic.These graphs are isomorphic, since each is the 3-cycle.These graphs are not isomorphic, since they are of different shape.These graphs are isomorphic, since each is the 5-cycle.Find the strongly connected components of this graph?b{a, b, c, d, e, f, g, h}.None of them.{a, b, c, d}, {e, f, h}, and {g}.{a, b, c, d, e, h}, {f}, and {g}.{a, b, c, d}, {e, g, h}, and (f}.

The only first question will be answered. 1 The above two graphs are isomorphic. Consider f is a…

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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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Given a vertex set W = {1, 2, 3, 4}, solve for the following questions: (i) Knowing that edges are the same if and only if they have the same endpoint, how many different edges are possible? (ii) Suppose for this question that graphs are different if they have different sets of edges (they do not depend on if the graphs are isomorphic or not). How many simple graphs are there with the vertex set W? (iii) Draw the eleven nonisomorphic simple graphs that have four vertices.
For the following simple graphs G_1=(V_1,E_1)G1=(V1,E1) and G_2=(V_2,E_2)G2=(V2,E2) (described by their vertex and edge sets) decide whether they are isomorphic. If they are then prove it, and if they are not give a convincing argument that explains why not: V_1=\{ a,b,c,d,e,f,g,h\}V1={a,b,c,d,e,f,g,h}, E_1=\{ ac,ag,ah,bc,bd,bh,ce,de,df,fg,fh\}E1={ac,ag,ah,bc,bd,bh,ce,de,df,fg,fh}, V_2=\{ 1,2,3,4,5,6,7,8\}V2={1,2,3,4,5,6,7,8}, E_2=\{ 12,15,16,25,27,34,36,37,38,48,67\}E2={12,15,16,25,27,34,36,37,38,48,67}
Exercise 1 In each of the following questions V=[n]={1,2,...,n}. What is the number of (simple undirected) graphs G=(V,E) ? What is the number of (simple undirected) graphs G=(V,E) with no isolated vertices ? Prove your answers and show your work step by step
In each of the following questions V=[n]={1,2,...,n}. What is the number of (simple undirected) graphs G=(V,E) ? What is the number of (simple undirected) graphs G=(V,E) with no isolated vertices ? Prove your answers and show your work step by step
Are the following graphs isomorphic or non-isomorphic? Show the complete steps to prove or disapprove
An Euler path, in a graph or multigraph, is a walk through the graph which uses every edge exactly once. An Euler circuit is an Euler path which starts and stops at the same vertex. NOTE: graphs are in the image attached. Which of the graphs below have Euler paths? Which have Euler circuits? List the degrees of each vertex of the graphs above. Is there a connection between degrees and the existence of Euler paths and circuits? Is it possible for a graph with a degree 1 vertex to have an Euler circuit? If so, draw one. If not, explain why not. What about an Euler path? What if every vertex of the graph has degree 2. Is there an Euler path? An Euler circuit? Draw some graphs. Below is part of a graph. Even though you can only see some of the vertices, can you deduce whether the graph will have an Euler path or circuit? NOTE: graphs is in the image attached.
For the following simple graphs G=(V,E) (described by their vertex and edge sets) decide whether they are bipartite or not. If G is bipartite, then give its bipartition, and if it is not explain why. 1) V={a,b,c,d,e,f,g}, E={ag,af,ae,bf,be,bc,dc,dg,df,de} 2) V={a,b,c,d,e,f,g,h}, E={ac,ad,ah,bc,bh,bd,ec,ef,eg,hf,hg}
PLEASE TYPE ONLY IF NOT TYPE THAN DO NOT DO IT*** ONLY DO EXCERCISE B ON 8.4.3***** PLEASE DO ALL THREE PROBLEMS*** D AND E FOR 6.1.4 & B FOR 8.4.3 Exercise 6.1.4: Reasoning about common graphs. (d) For what value of n is Q2 = Cn? (e) Is Qn a regular graph for n ≥ 1? If so, what is the degree of the vertices in Qn?
Does there exist a simple graph with five vertices of the following degree? If so, draw such a graph. 0, 1, 2, 2, 3
A complete graph has no loops, and each of its vertexes is adjacent to all its other vertexes. Which complete graphs (if any) are bipartite? Which complete graphs (if any) are not bipartite? Prove that your answers are correct. Hints: think about proofs by cases and graph coloring.
Is it true or false? If it is true, include a (short, but clear) argument why it is true, and if it is false, include a concrete graph which shows that the claim is false.a) If all vertices in a connected graph have even degree, then for whichever two vertices u and v in the graph you choose, there is an Eulerian trail between u and v. b) Given a graph G we construct a new graph H by adding a new vertex v and edges between v and every vertex of G. If G is Hamiltonian, then so is H.c) We know that if a graph has a walk between u and v it also has a path between u and v, for any two vertices u and v. Is it always true that if a graph has a circuit containing u and v it also has a cycle containing u and v? d) The complete bipartite graph K?,?(lowered indicies) is Hamiltonian if and only if m = n ≥ 2.
5. (This question goes slightly beyond what was covered in the lectures, but you can solve it by combining algorithms that we have described.) A directed graph is said to be strongly connected if every vertex is reachable from every other vertex; i.e., for every pair of vertices u, v, there is a directed path from u to v and a directed path from v to u. A strong component of a graph is then a maximal subgraph that is strongly connected. That is all vertices in a strong component can reach each other, and any other vertex in the directed graph either cannot reach the strong component or cannot be reached from the component. (Note that we are considering directed graphs, so for a pair of vertices u and v there could be a path from u to v, but no path path from v back to u; in that case, u and v are not in the same strong component, even though they are connected by a path in one direction.) Given a vertex v in a directed graph D, design an algorithm for com- puting the strong connected…