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Which of the following graphs are bipartite? H OA H OC X X S A G T

Which of the following graphs are bipartite? H OA H OC X X S A G T

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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**Question:** Which of the following graphs are bipartite? **Graph A:** - This graph consists of two groups of vertices connected by edges: Group 1 includes vertices {S, T, U, V, W, H, X} and Group 2 includes vertices {R, Q}. **Graph B:** - This graph is a complete graph with vertices {A, B, C, D, E, F, G}, where each vertex is connected to every other vertex. **Graph C:** - This graph has vertices {S, T, U, V, W, H, X, R, Q} with multiple edges connecting them, forming various paths, but crossing edges suggest complexity in bipartite determination. **Graph D:** - This graph consists of two sets of vertices: Group 1 includes {P, O, N} and Group 2 includes {Q, R, S, T}, connected by edges between these groups. There are no edges connecting vertices within the same group. **Check Boxes:** - □ A - □ B - □ C - □ D **Explanation:** A bipartite graph is one in which the vertex set can be divided into two disjoint sets such that no two graph vertices within the same set are adjacent.
Transcribed Image Text:**Question:** Which of the following graphs are bipartite? **Graph A:** - This graph consists of two groups of vertices connected by edges: Group 1 includes vertices {S, T, U, V, W, H, X} and Group 2 includes vertices {R, Q}. **Graph B:** - This graph is a complete graph with vertices {A, B, C, D, E, F, G}, where each vertex is connected to every other vertex. **Graph C:** - This graph has vertices {S, T, U, V, W, H, X, R, Q} with multiple edges connecting them, forming various paths, but crossing edges suggest complexity in bipartite determination. **Graph D:** - This graph consists of two sets of vertices: Group 1 includes {P, O, N} and Group 2 includes {Q, R, S, T}, connected by edges between these groups. There are no edges connecting vertices within the same group. **Check Boxes:** - □ A - □ B - □ C - □ D **Explanation:** A bipartite graph is one in which the vertex set can be divided into two disjoint sets such that no two graph vertices within the same set are adjacent.
**Transcription for Educational Website:** --- **Consider the following graph:** The provided graph is a pentagon-shaped complete graph with five vertices labeled as 'l', 'k', 'm', 'n', and 'o'. Each vertex is connected to every other vertex by edges, forming a complete graph, specifically denoted as \( K_5 \). --- **Question:** Which of the following graphs are subgraphs of the graph above? - A. \( P_2 \) - B. \( P_3 \) - C. \( K_5 \) - D. \( K_{1,4} \) - E. \( C_4 \) - F. \( K_{3,2} \) - G. \( K_6 \) --- **Graph Explanation:** The diagram shows all possible connections (edges) between the vertices, indicating it is a fully connected graph, \( K_5 \), where each of the 5 vertices is connected to every other vertex. Subgraphs of this graph include any smaller configurations of nodes and edges within this structure.
Transcribed Image Text:**Transcription for Educational Website:** --- **Consider the following graph:** The provided graph is a pentagon-shaped complete graph with five vertices labeled as 'l', 'k', 'm', 'n', and 'o'. Each vertex is connected to every other vertex by edges, forming a complete graph, specifically denoted as \( K_5 \). --- **Question:** Which of the following graphs are subgraphs of the graph above? - A. \( P_2 \) - B. \( P_3 \) - C. \( K_5 \) - D. \( K_{1,4} \) - E. \( C_4 \) - F. \( K_{3,2} \) - G. \( K_6 \) --- **Graph Explanation:** The diagram shows all possible connections (edges) between the vertices, indicating it is a fully connected graph, \( K_5 \), where each of the 5 vertices is connected to every other vertex. Subgraphs of this graph include any smaller configurations of nodes and edges within this structure.
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