A _______ is a connected, simple graph that has no cycles. Vertices of degree 1 in a tree are called the _______ of the tree. 3. The _______- graph on n nodes, denoted Kn, is the simple graph with nodes {1, . . . , n} and an edge between every pair of distinct nodes. 4. A graph is called ________ if its set of nodes can be partitioned into two disjoint sets S1 and S2 so that every edge in the graph has one endpoint in S1 and one endpoint in S2.

Q: Minimal Spanning Tree as an illustration or a textual list of edges (in our standard vertex order).

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A: I have solved below:

Q: D) What is the size of the graph? E) Find the shortest path distance from vertex F to vertex D.

A: Size of the graph is number of edges in the graph

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A: based on data structures

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A: Solved below:

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A: 3. True

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A: The solution is given in the next step

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A:

Q: Graph ? has 7 vertices and 21 edges, sum of the degrees of all its vertices is *

A: Given: -

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A: The Answer is

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A:

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A: Question:

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Q: A B F E D

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A: The Answer is

Q: Apply one algorithm on the graph below to find its minimum spanning tree. Describe the steps.

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A: Answer :

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A:

Minimum Spanning Tree

A spanning tree is a sub-graph of a connected, undirected graph. It has all the vertices of a graph with the minimum possible number of edges. If a vertex is skipped, then it will not be a spanning tree. The edges of a spanning tree may or may not have weights.