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Problem 6. Find all spanning trees of the graph below. How many different spanning trees are there? How many different spanning trees are there up to isomorphism (that is, if you grouped all the spanning trees by which are isomorphic, how many groups would you have)? a b с d f e

Problem 6. Find all spanning trees of the graph below. How many different spanning trees are there? How many different spanning trees are there up to isomorphism (that is, if you grouped all the spanning trees by which are isomorphic, how many groups would you have)? a b с d f e

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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**Problem 6.** Find all spanning trees of the graph below. How many different spanning trees are there? How many different spanning trees are there *up to isomorphism* (that is, if you grouped all the spanning trees by which are isomorphic, how many groups would you have)? The diagram depicts a graph with six vertices labeled \(a, b, c, d, e,\) and \(f\). The edges of the graph connect the vertices as follows: - Vertex \(a\) is connected to \(b, c,\) and \(d\). - Vertex \(b\) is connected to \(c\). - Vertex \(c\) is connected to \(d, f,\) and \(e\). - Vertex \(d\) is connected to \(e\). - Vertex \(f\) is connected to \(e\). To solve this problem, identify all possible subsets of edges that connect all vertices without cycles, which are the spanning trees of the graph. Furthermore, determine the number of unique spanning trees considering graph isomorphism, where trees are considered equivalent if they can be transformed into each other by renaming vertices.
Transcribed Image Text:**Problem 6.** Find all spanning trees of the graph below. How many different spanning trees are there? How many different spanning trees are there *up to isomorphism* (that is, if you grouped all the spanning trees by which are isomorphic, how many groups would you have)? The diagram depicts a graph with six vertices labeled \(a, b, c, d, e,\) and \(f\). The edges of the graph connect the vertices as follows: - Vertex \(a\) is connected to \(b, c,\) and \(d\). - Vertex \(b\) is connected to \(c\). - Vertex \(c\) is connected to \(d, f,\) and \(e\). - Vertex \(d\) is connected to \(e\). - Vertex \(f\) is connected to \(e\). To solve this problem, identify all possible subsets of edges that connect all vertices without cycles, which are the spanning trees of the graph. Furthermore, determine the number of unique spanning trees considering graph isomorphism, where trees are considered equivalent if they can be transformed into each other by renaming vertices.
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