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Linear Algebra: A Modern Introduction

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter3: Matrices

Section3.7: Applications

Problem 80EQ

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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.

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