A tree is a circuit-free connected graph. A leaf is a vertex of degree 1 in...

A tree is a circuit-free connected graph. A leaf is a vertex of degree 1 in a tree. Show that every tree T = (V, E) has the following properties: (a) There is a unique path between every pair of vertices. (b) Adding any edge creates a cycle. (c) Removing any edge disconnects the graph. (d) Every tree with at least two vertices has at least two leaves. (e) | V |=| E | +1.

Expert Solution

Colby Messinger answered 2 years ago

Discrete Mathematics A tree contains 1 vertex of degree 2, 1 vertex of degree 3, 1...

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1.Can you apply Theorem 13.6.12(A Vertex of Degree Five. If GG is a connected planar graph,...

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(a) What is the maximum degree of a vertex in a simple graph with n vertices?...

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find an alternative definition of the degree of a vertex of a graph. please be detailed...

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Prove that \strongly connected" is an equivalence relation on the vertex set of a directed graph

Suppose that a graph G is such that each vertex of G has degree at least...

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