Let G be a connected graph with degree sequence 3,4,5,6,7,8,9. Which of the followingis not true?[2](i) G is Hamiltonian but not Eulerian (ii) G is Eulerian but not Hamiltonian(iii) G is both Eulerian and Hamiltonian (iv) G is neither Eulerian nor Hamiltonian(v) none of the above

Hamiltonian Graph:A connected graph with n vertices is hamiltonian if degree of every vertex is ≥…

Answered: Let G be a connected graph with degree…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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please explain why the missing entires are 2,3,5
(1.2) Let Y = {Y,o} be a metric space. Suppose (pn) and (q,) are sequences in Y, where (9n) is a Cauchy sequence and o(pn; qn) → 0 as n → x. Show the following : (a) (Pn) is a Cauchy sequence in Y, (b) Pn + a if and only if q, → x.
8 Consider the following graph: b d T/F? The directed graph has an Euler circuit. [(Click to select) The directed graph has an Euler path. [(Click to select) The Euler path is (Click to select) (Click to select) a, d, b, d, e, b, e, c, b, d ΝΑ a, d, b, d, e, b, e, c, a, b a, d, b, d, e, b, e, c, b, a a, b, d, c, e, b, e, c, b, a T/F? (Choose "NA" if there is no Euler path.)
5. Let G = (V, E) be a bipartite graph with partite sets X and Y. Suppose X = {x₁,x₂,...,xn} and Y = {y₁, y2,...,Ym}. Show that Σdc(x₁) = |E|. i=1 m (HInt: Think graph fairy). (Also, note that Σdc(y;) = |E| as well, but just prove the above). j=1
19-
Question 4 Show that every u v walk in a graph contains au- v path. Question 5 [5.1] Prove or disprove that a graph and its complement cannot both be disconnected.. [5.2] Prove or disprove that if G is a connected graph, then its complement G is disconnected. Question 6 Consider the following graph G a b C d V}] e g h Determine the following (justify all your answers): 1. The order of G. 2. The size of G. 3. Two adjacent vertices in G. 4. Two nonadjacent vertices in G. 5. The open neighborhood of d. 6. The closed neighborhood of d. 7. The maximum degree of G. 8. The minimum degree of G. 9. The degree sequence of G. Question 7 During the Covid-19 lockdown, a group of 10 people met around a diner party. They each shook hands with each other, how many handshakes took place in that diner? Hint: Use vertices and edges. END
number 1
Let the degree sequence of a graph G be the sequence of length |V(G)| that contains the degrees of the vertices of G in non-increasing order. (a) For each of the following sequences, either draw a simple graph whose de- gree sequence is equal to that sequence, or explain why such a graph does not exist: (i) (4, 4, 4, 2, 2), (ii) (4, 2, 2, 1, 1), (iii) (3,3,3,2,1), (iv) (4, 3, 3, 2, 1), (v) (2, 2, 2, 1, 1).

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Let G be a connected graph with degree sequence 3,4,5,6,7,8,9. Which of the following is not true? [2] (i) G is Hamiltonian but not Eulerian (ii) G is Eulerian but not Hamiltonian (iii) G is both Eulerian and Hamiltonian (iv) G is neither Eulerian nor Hamiltonian (v) none of the above