Explanation Given: T Contains r , T has no simple circuits, and for every vertex v ∈ V other than r , deg − ( v ) = 1 in T Concept used: The minimum spanning tree is a simple circuit. Calculation: Consider a directed graph G = ( V , E ) and a sub graph T = ( V , F ) is an arborescence of G rooted at r . Since paths in trees are unique T contains all the vertices of G with all edges directed away from root. Thus the in- degree of each vertex except r is 1

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ISBN: 9781260521337

Author: ROSEN

Publisher: MCG

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Chapter 11, Problem 45SE

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a sub graph T(v,F) of the graph G=(V,E) is an arborescence of G rooted at r if and only if T contains r, T has no simple circuits, and for every vertex v∈V other than r,

deg−(v)=1 in T

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Chapter 11, Problem 44SE

Chapter 11, Problem 46SE

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Chapter 11 Solutions

DISCRETE MATHEMATICS+ITS APPL. (LL)-W/A

Ch. 11.1 - Prob. 1E Ch. 11.1 - Vhich of these graphs are trees?Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E

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a sub graph T ( v , F ) of the graph G = ( V , E ) is an arborescence of G rooted at r if and only if T contains r , T has no simple circuits, and for every vertex v ∈ V other than r , deg − ( v ) = 1 in T

Solution Summary: The author explains that a sub graph T(v,F) is an arborescence of G rooted at r for given conditions.

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To show:

a sub graph T(v,F) of the graph G=(V,E) is an arborescence of G rooted at r if and only if T contains r, T has no simple circuits, and for every vertex v∈V other than r,

deg−(v)=1 in T

Want to see the full answer?

Chapter 11 Solutions

a sub graph T ( v , F ) of the graph G = ( V , E ) is an arborescence of G rooted at r if and only if T contains r , T has no simple circuits, and for every vertex v ∈ V other than r , deg − ( v ) = 1 in T

Solution Summary: The author explains that a sub graph T(v,F) is an arborescence of G rooted at r for given conditions.

Videos

To show: a sub graph T(v,F) of the graph G=(V,E) is an arborescence of G rooted at r if and only if T contains r, T has no simple circuits, and for every vertex v∈V other than r, deg−(v)=1 in T

Want to see the full answer?

Chapter 11 Solutions

To show:

a sub graph T(v,F) of the graph G=(V,E) is an arborescence of G rooted at r if and only if T contains r, T has no simple circuits, and for every vertex v∈V other than r,

deg−(v)=1 in T