MAT3707 Assignment 3 (COMPLETE ANSWERS) 2024 (156556) - DUE 30 August 2024
MAT3707 Assignment 3 (COMPLETE ANSWERS) 2024 (156556) - DUE 30 August 2024
MAT3707 Assignment 3 (COMPLETE ANSWERS) 2024 (156556) - DUE 30 August 2024 ; 100% TRUSTED Complete, trusted solutions and explanations
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Discrete Mathematics: Combinatorics
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, MAT3707 Assignment 3 (COMPLETE ANSWERS) 2024
(156556) - DUE 30 August 2024 ; 100% TRUSTED
Complete, trusted solutions and explanations.
QUESTION 1 Consider the following two graphs: a b d c e f G1
u v w y x z G2 Are G1 and G2 isomorphic? A. Yes, because
they both have the same degree sequence. B. Yes, because
function g with g(a) = u, g(b) = v, g(c) = w, g(d) = x, g(e) = y,
and g(f) = z is an isomorphism. C. Yes, because function h with
h(a) = z, h(b) = w, h(c) = x, h(d) = y, h(e) = u, and h(f) = v is an
isomorphism. D. Yes, because they both have the same number
of vertices, the same number of edges and are both connected. E.
No, they are not isomorphic. QUESTION 2 Which of the
following is a necessary condition for a graph to be bipartite? A.
The graph has no odd cycles. B. The graph has even cycles. C.
The graph has an Euler cycle. D. The graph is planar. E. The
graph has a Hamiltonian circuit. QUESTION 3 In a connected
graph, if every vertex has an even degree, what can you
conclude? A. The graph has an Euler cycle. B. The graph is
planar. C. The graph has a Hamiltonian circuit. D. The graph is
bipartite. E. The graph is a tree. QUESTION 4 Which of the
following is NOT a property of a Hamiltonian circuit in a graph?
Page 2 A. It visits every vertex exactly once. B. It forms a cycle.
C. It forms a path. D. It must contain exactly two edges incident
to each vertex. E. It may contain repeated vertices. QUESTION
5 Consider the following graph: v2 v4 v5 v1 v3 Does this graph
have an Euler cycle? A. No, because there is no edge between
v1 and v5. B. No, because v3 does not have degree 2. C. No,
because it is not a complete graph. D. Yes, but not all edges
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