How many edges will a tree consisting of N nodes have? ans. Log(N) N – 1 N + 1 N

Break Down the Problem

1. Identify what a tree structure is: a connected and acyclic graph.
2. Understand the relationship between nodes and edges in a tree.

Relevant Concepts

1. In a tree, the relationship between the number of nodes $N$ and the number of edges $E$ can be expressed as: $E = N - 1$ where $E$ is the number of edges and $N$ is the number of nodes.

Analysis and Detail

1. For each additional node added to a tree, one edge is created to connect it to the existing structure.
2. Starting with one node, which has no edges, when you add the second node, one edge is formed, becoming two nodes with one edge.
3. Continuing this process, if we keep adding nodes, each requires an additional edge.

Verify and Summarize

The derived formula and reasoning are consistent: A tree with $N$ nodes will indeed have $N - 1$ edges. This relationship is fundamental in graph theory.

Final Answer

The number of edges in a tree consisting of $N$ nodes is $N - 1$.