Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 21.1, Problem 1E
Program Plan Intro
To list the vertices in each connected component after each iteration of CONNECTED-COMPONENETS procedure.
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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}
Without intersecting lines, draw the directed graph:
Where:
Let Y = {a, b, c, d, e}
Z = {(a, a), (b, a), (d, b), (d, c), (c, c), (e, a), (a, d), (c, e), (e, b), (b, d)}
let a graph have vertices h,i,j,k,l,m,n,o and edge set {{h,i},{h,j},{h,k},{h,n},{h,o},{j,k},{j,l},{j,m},{k,l},{m,o},.
on paper, draw the graph. then answer the questions below.
a. what is the degree of vertex k?
b. what is the degree of vertex h?
c. how many connected components does the graph have?
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- Given a graph G with N vertices, write a Matlab function with comments called ‘connectcheck.m’ to check the connectivity of the graph. The input should be the graph G and the output should be 1 if all vertices are connected and 0 if at least one vertex is not connected to the rest of the graph.arrow_forwardLet G be a connected graph that has exactly 4 vertices of odd degree: v1,v2,v3 and v4. Show that there are paths with no repeated edges from v1 to v2, and from v3 to v4, such that every edge in G is in exactly one of these paths.arrow_forwardHow many edges does a graph have if its degree sequence is 2, 4, 4, 5, 3?A. Draw a graph with the above listed sequence.B. Is it possible to draw an Euler Circuit with such a sequence of vertex degrees?Is it possible to draw an Euler Path? If yes, to either of these questions, draw the a graph that supports your answer.arrow_forward
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