Question

The sum of the weights of the edges in a path can be called all of the following EXCEPT ______.

a. length
b. weight
c. height
d. cost

Answer 1

In the context of graph theory, the sum of the weights of the edges in a path is known as the length, weight, or cost, but not the height, which is used to denote vertical measurement or the longest path from the root to a leaf in a tree.

Step-by-step explanation:

The sum of the weights of the edges in a path within a graph can be called several things depending on the context. Many terms are used interchangeably to describe this sum, including length, weight, and cost.

However, the term height isn't typically used in this context. The term height is often associated with trees in graph theory, where it refers to the longest path from the root node to a leaf node, or in general terms, as the vertical measurement.

Answer 2

The sum of the weights of the edges in a path can be called all of the following EXCEPT height (Option C).

Step-by-step explanation:

The sum of the weights of the edges in a path is referred to as the length, weight, or cost of the path, but not as the height. In graph theory, which is a part of discrete mathematics, these terms are commonly used to describe the total weight along a path in a weighted graph. Here are the correct terms and their explanations:

• Length: This is often used synonymously with the sum of the weights of the edges in a path.
• Weight: Similarly, it denotes the total sum of the weights of the edges in the given path.
• Cost: Yet another term that represents the total weight of the path, especially in contexts such as finding the least costly path.

However, the term height is not conventionally used in this context. It may refer to a vertical measure in a geometric or physical space rather than the sum of weights in a graph.

Thus, the correct option is C.