Question

Prove with example that every tree is a graph, but not every graph is a
tree.

Answer 1

Answer:

Every tree is a bipartite graph. A graph is bipartite if and only if it contains no cycles of odd length. Since a tree contains no cycles at all, it is bipartite. ... Every connected graph G admits a spanning tree, which is a tree that contains every vertex of G and whose edges are edges of G.

Edges: v − 1

Chromatic number: 2 if v > 1

Answer 2

Answer:

Every tree is a bipartite graph. A graph is bipartite if and only if it contains no cycles of odd length. Since a tree contains no cycles at all, it is bipartite. ... Every connected graph G admits a spanning tree, which is a tree that contains every vertex of G and whose edges are edges of G.

Edges: v − 1

Chromatic number: 2 if v > 1

Explanation:

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