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(3) (i) If a graph with 7 vertices has degrees 6, 4, 4, 3, 2, 1, d, what is the greatest value that d could have? Draw an example of a graph for which d takes this value. ive ers (ii) What is the greatest possible number of vertices of degree 1 in a tree with 11 vertices such that each vertex has degree at most 4? Draw an example of such a graph with this number of vertices of degree 1. Copy ask nas (iii) Let n 4 be an even integer. What is the greatest possible number of edges in a graph with n vertices that has a closed Euler trail? (Give your answer as an expression in terms of n.) For n=6, draw an example of such a graph with this number of edges.

(3) (i) If a graph with 7 vertices has degrees 6, 4, 4, 3, 2, 1, d, what is the greatest value that d could have? Draw an example of a graph for which d takes this value. ive ers (ii) What is the greatest possible number of vertices of degree 1 in a tree with 11 vertices such that each vertex has degree at most 4? Draw an example of such a graph with this number of vertices of degree 1. Copy ask nas (iii) Let n 4 be an even integer. What is the greatest possible number of edges in a graph with n vertices that has a closed Euler trail? (Give your answer as an expression in terms of n.) For n=6, draw an example of such a graph with this number of edges.

Principles Of Marketing
Principles Of Marketing
17th Edition
ISBN:9780134492513
Author:Kotler, Philip, Armstrong, Gary (gary M.)
Publisher:Kotler, Philip, Armstrong, Gary (gary M.)
Chapter1: Marketing: Creating Customer Value And Engagement
Section: Chapter Questions
Problem 1.1DQ
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(3) (i) If a graph with 7 vertices has degrees 6, 4, 4, 3, 2, 1, d, what is the greatest value that d could have? Draw an example of a graph for which d takes this value. ive ers (ii) What is the greatest possible number of vertices of degree 1 in a tree with 11 vertices such that each vertex has degree at most 4? Draw an example of such a graph with this number of vertices of degree 1. Copy ask nas (iii) Let n 4 be an even integer. What is the greatest possible number of edges in a graph with n vertices that has a closed Euler trail? (Give your answer as an expression in terms of n.) For n=6, draw an example of such a graph with this number of edges.
Transcribed Image Text:(3) (i) If a graph with 7 vertices has degrees 6, 4, 4, 3, 2, 1, d, what is the greatest value that d could have? Draw an example of a graph for which d takes this value. ive ers (ii) What is the greatest possible number of vertices of degree 1 in a tree with 11 vertices such that each vertex has degree at most 4? Draw an example of such a graph with this number of vertices of degree 1. Copy ask nas (iii) Let n 4 be an even integer. What is the greatest possible number of edges in a graph with n vertices that has a closed Euler trail? (Give your answer as an expression in terms of n.) For n=6, draw an example of such a graph with this number of edges.
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