Answer:

In the context of a node in a graph, an input node refers to a node that has only incoming branches, while an output node refers to a node that has only outgoing branches.

Graph Theory:
Graph theory is a branch of mathematics that deals with the study of graphs, which are mathematical structures used to represent relationships between objects. In a graph, nodes represent objects, and edges represent relationships between those objects.

Nodes and Branches:
In a graph, a node is a point that represents an object, while a branch refers to a connection or link between nodes. Each node can have multiple branches, which connect it to other nodes in the graph. The direction of a branch can be either incoming or outgoing, depending on whether it leads to or originates from a particular node.

Input Node:
An input node, also known as a source node or a root node, is a node in a graph that has only incoming branches. In other words, it is a node that does not have any branches leading outwards. It is called an input node because it is often considered as the starting point or the source of information in a graph.

Output Node:
On the other hand, an output node, also known as a sink node or a leaf node, is a node in a graph that has only outgoing branches. It is a node that does not have any branches leading inwards but only leads to other nodes. It is called an output node because it is often considered as the end point or the destination of information in a graph.

Example:
For example, let's consider a simple graph where nodes A, B, C, and D are connected through branches. If node A has branches leading to nodes B, C, and D, while nodes B, C, and D have branches leading to other nodes but not back to node A, then node A is an input node, and nodes B, C, and D are output nodes.

In this case, the correct answer is option 'A' because an input node is the term used to describe a node that has only incoming branches.