The symmetric difference graph of two graphs G. (V. E.) and G₂ (V₁ E₂) on Set is defined as E, DE ₂: = = E₁ G₁ DG₂:= (V, E, DE₂). 2 (E₁\E₂) U (E₂\E₁) E₂ €₁0 €₂ the same vertex If 6₁ and 6₂ are euleran, show that every Vertex in G, D G₂ has even degree FACT: Each vertex of even degree. a evlenan graph has SO show G D G₂ is eulerian.
The symmetric difference graph of two graphs G. (V. E.) and G₂ (V₁ E₂) on Set is defined as E, DE ₂: = = E₁ G₁ DG₂:= (V, E, DE₂). 2 (E₁\E₂) U (E₂\E₁) E₂ €₁0 €₂ the same vertex If 6₁ and 6₂ are euleran, show that every Vertex in G, D G₂ has even degree FACT: Each vertex of even degree. a evlenan graph has SO show G D G₂ is eulerian.
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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Question
![The symmetric difference graph of two graphs
G. (V. E.) and G₂ (V₁ E₂) on the same vertex
Set is defined as
G₁ AG₂:= (V, E, DE₂).
E₁ DE ₂ = (E₁ \ E₂) U (E₂\E.)
:
E₁
E₂
=
€₁ 0 € ₂
If G₁ and 6₂ are euleran, show that every
Vertex in G, D G₂ has even degree
FACT: Each vertex of a evlenan graph has
even degree.
SO: Show G₁ D G₂ is
eulerian.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40f1c26c-f7c8-4c93-b845-5cd503791479%2Ffb5e2269-085c-49f0-90c3-c859a5de94bc%2F01ygby_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The symmetric difference graph of two graphs
G. (V. E.) and G₂ (V₁ E₂) on the same vertex
Set is defined as
G₁ AG₂:= (V, E, DE₂).
E₁ DE ₂ = (E₁ \ E₂) U (E₂\E.)
:
E₁
E₂
=
€₁ 0 € ₂
If G₁ and 6₂ are euleran, show that every
Vertex in G, D G₂ has even degree
FACT: Each vertex of a evlenan graph has
even degree.
SO: Show G₁ D G₂ is
eulerian.
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Follow-up Question
Why do we subtract 'twice' every edge that is incident in the intersection?
Why is it 'three' even numbers that we are subtracting?
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