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In a tree, I want to refer to a particular child of a node, the child of this child, the child of this child of this child, and then the child of this child of this child of this child. For instance, in a binary tree, I would like to refer to the right sibling of the node, the right child of this one, etc..

Can I call these the first four rightmost immediate descendants of a node? Is the term "immediate" really clear?

Thank you very much.

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    $\begingroup$ What books or resources have you read and now you are reffering to? I am 100% sure that any resource starts from naming tree elements. Moreover, four means that you have some particular tree in mind - so this is not clear what structure you are talking about. $\endgroup$
    – Evil
    Commented Apr 14, 2016 at 15:24
  • $\begingroup$ Thanks @EvilJS I'm looking for the good term for speaking about contiguous descendants. I've not found this term. I would like to know if the term immediate is clear. Maybe I should call them the closest descendants. $\endgroup$
    – user7060
    Commented Apr 14, 2016 at 15:41
  • $\begingroup$ Maybe you could draw this tree? Tell about properties? If there is potential ambiguity, which are more immediate? $\endgroup$
    – Evil
    Commented Apr 14, 2016 at 21:28
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    $\begingroup$ I'm voting to close this question as unclear because the asker cannot clearly describe the concept they want a word for. $\endgroup$
    – David Richerby
    Commented Apr 15, 2016 at 15:22

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No, the phrase "the first four immediate descendants" doesn't say what you want. In particular, "first four" sounds like you're talking about four vertices, not four levels of vertices. If I read "immediate descendants" I'd be confused because it sounds like it should mean the same as "children" but surely you'd just say "children" if that's what you meant.

I would describe the vertices you want as being the set of all descendants of some node $v$ that are within distance $4$ of $v$. If you need to say it often and the number four is fixed, you could explicitly define a term such as "close descendants" to mean this.

Long story short, there's no standard term for the concept you want to describe so you must describe it explicitly and define any name you want to use for it.

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  • $\begingroup$ Thank you @DavidRicherby. In fact, when I say "first four descendants", I'm talking about a children of the node, the children of this children, the children of this children of this children, and then the children of this children of this children of this children. $\endgroup$
    – user7060
    Commented Apr 15, 2016 at 14:57
  • $\begingroup$ @user7060 OK, now I see what you mean. I edited your question and my answer. $\endgroup$
    – David Richerby
    Commented Apr 15, 2016 at 15:10
  • $\begingroup$ @user7060 I rolled back your edit (but corrected my typo). I know it's your question but your edit made it confusing. Every time you say "four descendants", everybody will read that as "four vertices", not "four levels of vertices". A "descendant" is a single vertex. $\endgroup$
    – David Richerby
    Commented Apr 15, 2016 at 15:12
  • $\begingroup$ Thanks very much. Is it better to use the term "closest" descendants, or "close" descendants ? $\endgroup$
    – user7060
    Commented Apr 15, 2016 at 15:15
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    $\begingroup$ OK, then I still don't understand what concept you're trying to explain. You wrote in your first comment that you were talking about a huge set of children, namely all descendants within distance four. Now you seem to be saying that you do just want to talk about four vertices after all. If that is what you mean, again, you need to say exactly which four. There is no concept of "first" in a tree, so you can't just say "the first four." You could try asking about this in Computer Science Chat but trying to figure this out in comments is going to be a nightmare. $\endgroup$
    – David Richerby
    Commented Apr 15, 2016 at 15:20
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There is no such name. The best way to describe what you want is, well, to specify it using language or mathematics. Don't expect an existing name for every concept you ever dream up; this is why we have language, so we can express novel concepts.

Personally, I don't find "the first four immediate descendants of a node" clear at all, so I'd suggest you define it more precisely. For instance, it's not clear what ordering you have in mind on the descendants, so "first four" doesn't seem well-defined.

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  • $\begingroup$ Thanks for your comments. I'm talking about a child, a grandchild, and a great-grandchild, etc. Can we use these terms with trees? $\endgroup$
    – user7060
    Commented Apr 15, 2016 at 15:00
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As others have stated there is no term for "first four" immediate descendants. However, if you have $n$ as a parent node, $n$ could have 4 children or 4 successors that branch from it.

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