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This question concerns subgraphs of graphs. In all cases, when we say G₁ is a subgraph of G₂, we mean that G₁ is isomorphic to some subgraph of G₂. Are the following statements true or false? ? ✓1. C3 is isomorphic to K3. ? ? 2 ? 2. If a graph is contains no cycles, then none of its subgraphs contain cycles. ✓3. C₁ is a subgraph of K₂,2. 4. Every bipartite graph is isomorphic to Km,n for some values of m and n. 5. P3 is a subgraph of K2,2. 6. C₁ is a subgraph of P4.

This question concerns subgraphs of graphs. In all cases, when we say G₁ is a subgraph of G₂, we mean that G₁ is isomorphic to some subgraph of G₂. Are the following statements true or false? ? ✓1. C3 is isomorphic to K3. ? ? 2 ? 2. If a graph is contains no cycles, then none of its subgraphs contain cycles. ✓3. C₁ is a subgraph of K₂,2. 4. Every bipartite graph is isomorphic to Km,n for some values of m and n. 5. P3 is a subgraph of K2,2. 6. C₁ is a subgraph of P4.

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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This question concerns subgraphs of graphs. In all cases, when we say G₁ is a subgraph of G₂, we mean that G₁ is isomorphic to some subgraph of G₂. Are the following statements true or false? ? ✓1. C3 is isomorphic to K3. ? ? 2 ? 2. If a graph is contains no cycles, then none of its subgraphs contain cycles. ✓3. C₁ is a subgraph of K₂,2. 4. Every bipartite graph is isomorphic to Km,n for some values of m and n. 5. P3 is a subgraph of K2,2. 6. C₁ is a subgraph of P4.
Transcribed Image Text:This question concerns subgraphs of graphs. In all cases, when we say G₁ is a subgraph of G₂, we mean that G₁ is isomorphic to some subgraph of G₂. Are the following statements true or false? ? ✓1. C3 is isomorphic to K3. ? ? 2 ? 2. If a graph is contains no cycles, then none of its subgraphs contain cycles. ✓3. C₁ is a subgraph of K₂,2. 4. Every bipartite graph is isomorphic to Km,n for some values of m and n. 5. P3 is a subgraph of K2,2. 6. C₁ is a subgraph of P4.
1. How many edges does the cycle graph C₁5 have? 2. How many edges does the star graph S18 have? (Hint; the star graph S is the same as the complete bipartite graph K₁,k) 3. How many edges does the complete graph K₁ have? 4. How many edges does the complete bipartite graph K3,4 have?
Transcribed Image Text:1. How many edges does the cycle graph C₁5 have? 2. How many edges does the star graph S18 have? (Hint; the star graph S is the same as the complete bipartite graph K₁,k) 3. How many edges does the complete graph K₁ have? 4. How many edges does the complete bipartite graph K3,4 have?
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