Is there a term for an adult without children, similar to "orphan" for the other way around?

Solution 1:

From an English language perspective, there is nothing wrong with the word childless:

[Lexico (Oxford Dictionaries)]
Not having any children.
‘a childless couple’
‘I am childless by choice’
‘For them, a childless marriage is considered a great misfortune.’
‘He left her a childless widow at the age of eighteen.’

However, the word orphan implies a child whose parents have died unnaturally or unexpectedly. Childless covers the state of being without children, but not specifically having had a child who died unnaturally or unexpectedly.

On the other hand, in terms of the niche-specific language of computing, you might want to use leaf node.

From Wikipedia's entry on Node (computer science) (the text in bold is my own emphasis):

• Child: A child node is a node extending from another node. For example, a computer with internet access could be considered a child node of a node representing the internet. The inverse relationship is that of a parent node. If node C is a child of node A, then A is the parent node of C.
• Degree: the degree of a node is the number of children of the node.
• Depth: the depth of node A is the length of the path from A to the root node. The root node is said to have depth 0.
• Edge: the connection between nodes.
• Forest: a set of trees.
• Height: the height of node A is the length of the longest path through children to a leaf node.
• Internal node: a node with at least one child.
• Leaf node: a node with no children.
• Root node: a node distinguished from the rest of the tree nodes. Usually, it is depicted as the highest node of the tree.
• Sibling nodes: these are nodes connected to the same parent node.

Solution 2:

If you google “reverse orphan”, you get a huge amount of hits. Apparently, this is a common question in the English language. Interestingly, this same question was asked on ELL back in 2014, and here in 2012 (which is why I marked this question as a duplicate, but am going to posit an answer here).

A number of neologisms have been suggested. For example:

• naphro, from a TVTropes discussion (as the reverse of orphan).
• Perspoiled, from the same TVTropes discussion, “;from the Latin "puer spoliari" which means "robbed of child", according to Google Translate.”

Recently, the term elder orphan seems to have been used to describe older people without children. However, I think this is imprecise (how do you distinguish this use from 2 child orphans, an elder and younger)?

As noted, from a strictly technical standpoint, you would use the term leaf (as in leaf node), to describe a node with no children. Of course, this would accurately describe a node that has never had a child. When talking about an orphaned node, we generally mean a node missing its parent/context (as apposed to a leaf node, which is perfectly fine). When referring to trees, we can perhaps use the typesetting convention of widows and orphans.

In some places, the Sanskrit word vilohmah seems to have been picked up to describe this situation.

Solution 3:

In a graph, you might call these terminal nodes, or leaves (see for instance this document on a proposed text-encoding standard for graphs https://www.tei-c.org/release/doc/tei-p5-doc/en/html/GD.html).