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.

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A: 3. True

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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.