GRAPH THEORY 2. Consider the following graph and the associated subgraphs Determ

Question

GRAPH THEORY 2. Consider the following graph and the associated subgraphs Determine whether or not each subgraph is a spanning tree. b. B. Use the method derived from Prim's algorithm to determine the minimal spanning tree for the following graph. Remember the process: Select the edge with the least weight to initiate the process; then include into the tree the edge whose weight is equal to the preceding weight or is the next larger weight. Continue in this manner, but do not form a cycle or a disconnected graph in the process. Copy the duplicate set of vertices to the right of the graph, draw the minimal spanning tree, and find its value. 3.

Explanation / Answer

Solution 2 :

Subgraph 'a' is not a spanning tree because it is containing a cycle i.e. ACDEA

Similarly, Subgraph 'b' is also not a spanning tree because it is also containing a cycle i.e. FBDF and another thing is that, subgraph 'b' is not connected with vertex 'E' , it means that subgraph 'b' is not connected with all the vertex.

While Subgraph 'c' and subgraph 'd' both are Spanning tree because both subgraphs are containing all the vertices of the given graph without any cycle.

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