If there is no edge from two vertex is the length infinity
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In graph theory, a graph consists of vertices (or nodes) and edges (connections between the vertices). Show more…
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Let G be a simple graph with n vertices, and suppose that d(v) + d(w) >= n - 1 for all pairs of distinct non-adjacent vertices v, w. Show that any two vertices of G are connected by a path of length at most 2. (In particular, G is connected.)
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Question 3 Do the following: 1. Prove that in a finite directed graph if every edge has at least one outgoing edge, then the graph contains a cycle. Hint: Consider the longest path in the graph. 2. Give an example of a directed graph with infinitely many vertices in which each vertex has at least one outgoing edge, but the graph has no cycles.
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