trees are about the most basic data structure that you're ever going to come across there they pervade computer science and other subjects so let's talk about them and the simplest definition of a tree is that a tree is a connected graph with no cycles in this setting we're talking about simple graphs and trees with undirected edges well in order to make sense out of that we'd better have a definition of a cycle there's a picture of a typical tree but to be precise what's a cycle in a simple graph well it's a closed walk of length greater than 2 that doesn't cross itself so the not crossing itself is the standard definition of a cycle that we were using in a directed graph it simply means that it's a path except that the beginning and end vertex are the same so it looks like you start someplace at V and then you go around to a and to W and it's all distinct vertices as you go around in this path except that the path ends where it starts at V which is what keeps it from being a path it makes it a cycle now the length greater than 2 is what is the difference between the definition of cycle between simple graphs and directed graphs in a directed graph it's perfectly possible to have a self-loop of length 1 that is an interesting and important kind of cycle to have but we forbid them in simple graphs because there's no way to avoid having a cycle of length 2 because you always have the ability to go back and forth and cross an edge that's not interesting and so we don't consider that to be a cycle a cycle then has to be of length greater than 2 it also rules out the cycle of length 0 which you get by taking a vertex or by itself ok with that technical definition we now know what a cycle is in this simple graph and we understand the definition of tree here are some more pictures of trees simple graphs with no cycles now they really come up all the time and why is that well there are family trees which you may be familiar with where you're during a picture of the descendants of a given person and they keep branching out in a you know tree structure as traditionally displayed there are search tree which come up the whole time in computer science where you branch on the answer to some question which tells you which way to search next there are game trees which we've already discussed in this class which are used to define great games and strategies their parse trees that come up in in compiler technology and in language theory and in the responding trees which we're going to be talking about some today now there in addition to these places where trees come up there are a lot of different kinds of trees there's rooted trees where there's some designated vertex called the root and you think of getting to all the other vertices from the road there are ordered trees where when you're at a given vertex there's a distinct order in which you are going to be in which the exit edges from a vertex are there's a first one in the second one the third one or a left one in the next leftmost and so on so that there's an order in which you can choose to leave the vertex there are binary trees in which each vertex has sort of two ways out exactly or no ways out if it's a so-called leaf and then there are complete trees whose definition olive is not important to us because we're not going to consider any of these there's also by the way directed trees in which edges are have a direction as in a digraph tree but we're not considering any of these we're going to focus on so-called pure trees which are unordered unrooted undirected and that's what we're talking about so let's examine some more properties of trees and equivalent definitions of trees it will be important for theoretical reasons and convenience to know lots of different characterizations of trees so we've starting off in the definition which says it's a connected simple graph with no cycles but there's other ways to characterize it so an edge in a simple graph is called a cut edge if when you remove it from the graph two vertices that used to be connected that is used to have a path between them cease to have a path between them so here's a we'll graph illustration and that edge e is a cut edge because if I delete it then there are now two components there used to be two vertices actually any of the vertices here used to be connected to any of the vertices there via that edge but once I've deleted that edge all of those vertices here and there that used to be connected no longer are so that makes via cut edge Oh F is not a cut edge because even if I delete edge F there is in fact still a path from every vertex to every other vertex here so that F is not disconnecting anything um and as I say it's still connected after you delete it so now we get a simple way to characterize trees in terms of cut edges because an edge is not a cut edge if and only if it's on a cycle if you think about that if it's on a cycle and you cut an edge out of a cycle then everything on the cycle still connected by going the other way around the cycle that doesn't use that edge and if it's not on a cycle then in fact you can think through that deleting it means that there's not going to be two paths between two things that it's at its endpoints and so it will separate them okay so another way then to define a tree is to say a tree is a connected graph where every edge is a cut edge then as soon as you cut any edge out of a tree it stops being connected that yields another way to say that something is a tree a tree is a simple graph that is connected and is edged minimal which again means that if you remove any edge it stops having that property of being connected so it's an edge minimal connected graph that's kind of the reason why trees are so important because if you're trying to figure out a way to get a whole bunch of things a whole bunch of vertices connected a tree is gonna have the minimum number of edges that are sufficient to get them all connected if you think about different nodes in a network that need to communicate with each other and you want to know how many direct connections do there have to be between these communication centers in order for everybody to talk to everybody else the answer is it's got to be a tree on n vertices and a tree on n vertices is going to have exactly n minus 1 edges so that gives you I still another equivalent definition of a tree a tree is a connected graph that has n vertices and n minus 1 edges a kind of dual way to think about it is that a tree is an acyclic graph that has as many edges as it possibly could without having any cycles so typically an acyclic graph might not be connected but as long as it's not connected you can keep adding edges that will connect things up without creating cycles but the minute you get a tree so that everything is connected you can't add another edge so an edge 'men an edge maximal acyclic graph is still another way to characterize trees and maybe the most useful way is to say that a graph in which there is a unique path between any two vertices is a tree so of course if there's a unique path in particular isn't passed so all the vertices have to be connected but what makes it a tree is that there aren't two different ways to connect between two vertices because as soon as the word that would be a cycle and those are some of the basic ways that trees can be formulated equivalently and in fact there's lots more but this is enough for today

### Family Trees: How to Add Stillborn Children to FamilySearch & Ancestry

Is a story of a mother complete if we do

not record the identity of her stillborn children? Today I'm going to show you how you

can add stillborn children to the family tree so you can make sure you're telling the

complete story about the females on your family tree. Whenever you are recording the

birth of any child, it is important that you use documentation. And particularly when you

are trying to document a stillborn child, you want to base this information on some type of

documentation. Now there are not a lot of records that are created for stillbirths. There are some,

and I'll show you one in just a moment. However, you can utilize interviews with people. You could

use family bibles occasionally the stillborn child is recorded there. You can also utilize

diaries and other first-hand accounts about the loss of a child just.

Be sure to tell other

people what sources you use and, if possible, share those images when you start recording that

there was a stillborn child in your family tree. Over in Ohio, as you can see on the Ohio History

Connection page, which is associated with the Ohio State Archives, there is a death index. And

one of the things they have – Because I remember being in the state archive and going past this

collection. Unfortunately, it didn't have enough time to explore it. However, I now can search an

index to this collection using the search form. In this collection, I went ahead and used the name

stillborn. and then I have to have part of a last name. So I'm just going to use a wildcard search.

And then I'm going to limit it to franklin county. And do a search range. It's pretty broad, but

I'm going to go ahead and use it 1913 to 1935. and click search.

Now I find that there are

quite a few of the stillborns recorded. This is their volume number and their certificate.

And I can go and look those up. So, I do have evidence that a stillborn child was born with

the last name Brauwnex, possibly even Broadway, in Franklin County, Ohio. And I have the

date. Now that you know that you have evidence of a stillborn child born to a woman,

what do you do? Well, you're going to add that to the FamilySearch family tree. So, let's

say that for my Grandma Emma, there is a record that said that when Lewis

was born, she had had nine children. Now I have one child that she recorded in

her Bible, but this is not a stillborn death. I did have another record in 1904 about a child

dying.

I did find that certificate, and there's still a few other children to add to this tree.

So, I click "Add a child." You simply add a child as you would if you had a living birth. So, now

I'm going to click on "Add a child." And now I'm going to put in the name. I don't know the name of

the child. So, I'm not going to put a first name. I do know that the father's name was Brown. So,

I'm going to do that. The child was male. They are deceased. And now I need to put the birth date

and the birth year. So, let's say 18 November 19 in Columbus, Ohio. And then it's the same

date, and place/ I just did a copy and ctrl+c copy. Control+v paste. And I went ahead and click

next.

Now it's going to search the database to see if I already have a match in there. I don't. So,

I'm going to click "Create a Person." And now I have the child in 1905, but how does anybody

know that that child is a stillborn? Well, I need to go to the profile, and here I can click

"Edit." Now you can add information. In this case, perhaps you knew that the child was stillborn at

three months old or the child was stillborn at eight months old. There are a lot of the records

that actually tell you how far along in the pregnancy what the mother was. So, if you have

it, go ahead and put it in. Then click "Save." And that's one way you can add a stillborn.

Another thing you could do is do add an EVENT here on FamilySearch. And they do

have a custom event for stillborn. And then you put in the place- Franklin County,

Ohio – and then tell people where you got this information.

So, there you go. So in FamilySearch,

you have a note, and you have a custom field for putting a stillbirth. What are you going to add

to your family tree about your stillborn child? Anything you have access to. So, the child's name,

but we'll give you some guidelines about that in just a minute. You're going to add the gender.

You're going to add the birth date and place, and the death date and place. And then attach

any sources that you know that articulates this information. Now some records do not differentiate

between a child that is born and is deceased or a child that is born and lives for a few

hours and then dies. So, do your best based on the records that you have. Don't put your

own presumptions into the records.

If it says stillborn, that's what you go with. If it does not

say stillborn, do not add a stillborn tag for a child that dies the same day that they were born.

Try to be as clear as you can. Now I'm over on Ancestry. And there's actually one cool thing that

I wish a lot of platforms has, and that is the way to tag your ancestor. So, you're not cluttering up

the suffix field with this extraneous information or adding crazy graphics. So, all you have to do

is click on MyTreeTags.

If the child died young, so, it lives for a few hours, live for a

few days, then you can put the "Died Young: relationship tree tag onto your tree. And notice

it'll just be there in your profile. So, whenever you come across this child, you can see, "oh,

they died young." If they did not die young, then you're going to need to add a custom MyTreeTag.

So, to do that, you create a custom tree tag "Stillborn" and click "Create." And now you have

STILLBORN attached to that tree.

And you can attach it to anybody else in your family tree

that is a stillborn child. So, how do you record the name of your stillborn child? Consult the

documents. If a document says the child's name is Lizzie Brown, then you name the child Lizzie

Brown. Becareful. Just because it says Lizzie, does not mean their name is Elizabeth. Use what

is on the documents that are available to you. If you do not have a name identified on a

document, or the document says something that's "infant," "girl," "boy," "unnamed," or

"stillborn," do not put them in your tree. So, in this tree, it has Miss. And Miss should not be

in that field. Then you have the gender. And you can go ahead and click "Save." Now back to naming,

if the father was named on the certificate, the genealogical standard is that you use

the father's surname as the stillborn child's surname. So, in this case, Geiszler, because I

do know that George Joseph Geisler was married to Eveline Townley Peak at this time period. So, the

last name would be Geiszler.

But not every mother identifies the name of a father. And in that

case, then you would just use the mother's surname in place of the father's surname for the surname

of a child. Now, if you have a stillborn child and you have no identity for the parents, I don't know

how you're going to put that into the family tree. Because you're just going to have a floating

tree out there of this child with no parents' names. So, I would refrain from adding a stillborn

child with no known parents to the family tree.

If you do know them, then follow those practices. If

you have other questions, don't be afraid to ask how do I add fill in the blank to my family

tree, and I'll be happy to answer you. If you want more tips and tricks on how to

get started in genealogy research, be sure to check out this video. And if you're ready for

something new, check out this video right here. What are the things that you're? What

are you going to add to the family?