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Let G(r, s) be the graph with vertex set V= {(a,b) e Zx Z|1

Let G(r, s) be the graph with vertex set V= {(a,b) e Zx Z|1

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let C(r, s) be the graph with vertex set V- {(a,b) e Z x Z|1<a<r,1<b< s} and edge set E = {(a,b), (c, d)} | (a, b), (e, d) e V, le –a| + |d – b} = 1} for any integers r, s > 2 For example, the graph G(3, 4) looks like the following, (1.1) (1,2) (1,3) (1,4) (2,1) (2,2) (2,3) (2,4) (3,1) (3,2) (3,3) (3,4) Flynn is interested in studying graphs of this type, and is especially keen to look into certain properties they can have la) Find all values of r, s for which G(r, s) has an Euler path or an Euler circuit. Explain your answer.
Transcribed Image Text:Let C(r, s) be the graph with vertex set V- {(a,b) e Z x Z|1<a<r,1<b< s} and edge set E = {(a,b), (c, d)} | (a, b), (e, d) e V, le –a| + |d – b} = 1} for any integers r, s > 2 For example, the graph G(3, 4) looks like the following, (1.1) (1,2) (1,3) (1,4) (2,1) (2,2) (2,3) (2,4) (3,1) (3,2) (3,3) (3,4) Flynn is interested in studying graphs of this type, and is especially keen to look into certain properties they can have la) Find all values of r, s for which G(r, s) has an Euler path or an Euler circuit. Explain your answer.
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