Running Complete bipartite graphs. A complete bipartite graph is a graph having the property that the vertices of the graph can be divided into two groups A and B and each vertex in A is adjacent to each vertex in B, as shown in Fig 5-64 . Two vertices in A are never adjacent, and neither are two vertices in B. Let m and n denote the number of vertices in A and B, respectively, and assume m ≤ n . Figure 5-64 a. Describe all the possible values of m and n for which the complete bipartite graph has an Euler circuit. ( Hint: There are infinitely many values of m and n. ) b. Describe all the possible values of m and n for which the complete bipartite graph has an Euler path.
Running Complete bipartite graphs. A complete bipartite graph is a graph having the property that the vertices of the graph can be divided into two groups A and B and each vertex in A is adjacent to each vertex in B, as shown in Fig 5-64 . Two vertices in A are never adjacent, and neither are two vertices in B. Let m and n denote the number of vertices in A and B, respectively, and assume m ≤ n . Figure 5-64 a. Describe all the possible values of m and n for which the complete bipartite graph has an Euler circuit. ( Hint: There are infinitely many values of m and n. ) b. Describe all the possible values of m and n for which the complete bipartite graph has an Euler path.
Solution Summary: The author explains that a connected graph has an Euler circuit if all vertices are even.
Complete bipartite graphs. A complete bipartite graph is a graph having the property that the vertices of the graph can be divided into two groups A and B and each vertex in A is adjacent to each vertex in B, as shown in Fig 5-64. Two vertices in A are never adjacent, and neither are two vertices in B. Let m and n denote the number of vertices in A and B, respectively, and assume
m
≤
n
.
Figure 5-64
a. Describe all the possible values of m and n for which the complete bipartite graph has an Euler circuit. (Hint: There are infinitely many values of m and n.)
b. Describe all the possible values of m and n for which the complete bipartite graph has an Euler path.
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