Draw an example of each of the following on at least 3 vertices, or state it cannot exist. Briefly justify your answers. Bonus points for interesting examples. (a) A pseudograph with both an eulerian circuit and a Hamilton cycle (b) A regular pseudograph with both an eulerian circuit and a Hamilton path, but no Hamilton cycle (c) A pseudograph with both an eulerian trail and a Hamilton path, but no eulerian circuit or Hamilton cycle (d) A pseudograph with an eulerian trail and an odd number of edges (e) A graph (not a pseudograph) with two Hamilton cycles that don't share any edges

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter12: Queueing Models
Section12.5: Analytic Steady-state Queueing Models
Problem 13P
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solve this graph therory problem
Draw an example of each of the following on at least 3 vertices, or state it cannot exist. Briefly
justify your answers. Bonus points for interesting examples.
(a) A pseudograph with both an eulerian circuit and a Hamilton cycle
(b) A regular pseudograph with both an eulerian circuit and a Hamilton path, but no Hamilton
cycle
(c) A pseudograph with both an eulerian trail and a Hamilton path, but no eulerian circuit
or Hamilton cycle
(d) A pseudograph with an eulerian trail and an odd number of edges
(e) A graph (not a pseudograph) with two Hamilton cycles that don't share any edges
Transcribed Image Text:Draw an example of each of the following on at least 3 vertices, or state it cannot exist. Briefly justify your answers. Bonus points for interesting examples. (a) A pseudograph with both an eulerian circuit and a Hamilton cycle (b) A regular pseudograph with both an eulerian circuit and a Hamilton path, but no Hamilton cycle (c) A pseudograph with both an eulerian trail and a Hamilton path, but no eulerian circuit or Hamilton cycle (d) A pseudograph with an eulerian trail and an odd number of edges (e) A graph (not a pseudograph) with two Hamilton cycles that don't share any edges
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