Graphs i. Draw a connected bipartite graph with 6 labelled vertices, {a, b, c, d, e, f} = V and 5 edges. Based on the graph you’ve drawn, give the corresponding partition π = {V1, V2} and the relation ρ ⊂ V1 × V2 corresponding with the edges. ii. Let A be a set of six elements and σ an equivalence relation on A such that the resulting partition is {{a, c, f}, {b, e}, {d}}. Draw the directed graph corresponding with σ on A. iii. Draw a directed graph with 5 vertices and 10 edges (without duplicating any edges) representing a relation ρ that is reflexive and antisymmetric, but not symmetric or transitive. Note how these properties can be identified from the graph.
Graphs i. Draw a connected bipartite graph with 6 labelled vertices, {a, b, c, d, e, f} = V and 5 edges. Based on the graph you’ve drawn, give the corresponding partition π = {V1, V2} and the relation ρ ⊂ V1 × V2 corresponding with the edges. ii. Let A be a set of six elements and σ an equivalence relation on A such that the resulting partition is {{a, c, f}, {b, e}, {d}}. Draw the directed graph corresponding with σ on A. iii. Draw a directed graph with 5 vertices and 10 edges (without duplicating any edges) representing a relation ρ that is reflexive and antisymmetric, but not symmetric or transitive. Note how these properties can be identified from the graph.
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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Graphs
i. Draw a connected bipartite graph with 6 labelled vertices, {a, b, c, d, e, f} = V and 5 edges. Based on the graph you’ve drawn, give the corresponding partition π = {V1, V2} and the relation ρ ⊂ V1 × V2 corresponding with the edges.
ii. Let A be a set of six elements and σ an equivalence relation on A such that the resulting partition is {{a, c, f}, {b, e}, {d}}. Draw the directed graph corresponding with σ on A.
iii. Draw a directed graph with 5 vertices and 10 edges (without duplicating any edges) representing a relation ρ that is reflexive and antisymmetric, but not symmetric or transitive. Note how these properties can be identified from the graph.
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