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= Two graphs G = (V, E) and H (W, F) are called isomorphic if there exists a bijection f : V→ W such that any two vertices u and w of V are adjacent in G if and only if their images f(u) and f(v) are adjacent in H. In other words two graphs are isomorphic are the same up to some relabelling of their vertices. Draw the eleven non-isomorphic graphs on four vertices. Hint: if n; denotes the number of non- isomorphic graphs on four vertices with i edges then (no, n₁, ..., n6) = (1, 1, 2, 3, 2, 1, 1).

= Two graphs G = (V, E) and H (W, F) are called isomorphic if there exists a bijection f : V→ W such that any two vertices u and w of V are adjacent in G if and only if their images f(u) and f(v) are adjacent in H. In other words two graphs are isomorphic are the same up to some relabelling of their vertices. Draw the eleven non-isomorphic graphs on four vertices. Hint: if n; denotes the number of non- isomorphic graphs on four vertices with i edges then (no, n₁, ..., n6) = (1, 1, 2, 3, 2, 1, 1).

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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Two graphs G = (V, E) and H= (W, F) are called isomorphic if there exists a bijection f : V → W such that any two vertices u and w of V are adjacent in G if and only if their images f(u) and f(v) are adjacent in H. In other words two graphs are isomorphic are the same up to some relabelling of their vertices. Draw the eleven non-isomorphic graphs on four vertices. Hint: if n; denotes the number of non- isomorphic graphs on four vertices with i edges then (no, n₁, ..., ‚ ná) = (1, 1, 2, 3, 2, 1, 1).
Transcribed Image Text:Two graphs G = (V, E) and H= (W, F) are called isomorphic if there exists a bijection f : V → W such that any two vertices u and w of V are adjacent in G if and only if their images f(u) and f(v) are adjacent in H. In other words two graphs are isomorphic are the same up to some relabelling of their vertices. Draw the eleven non-isomorphic graphs on four vertices. Hint: if n; denotes the number of non- isomorphic graphs on four vertices with i edges then (no, n₁, ..., ‚ ná) = (1, 1, 2, 3, 2, 1, 1).
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