0.2

0.4

0.6

0.8

Can I call them "even tenths"?

For example:

"If the maximum value in the data set is 1, then the values displayed in the bar graph are the ______." I am pertaining to the numbers above.

mydaruma25
2022-09-15
Answered

How can I describe the following numbers?

0.2

0.4

0.6

0.8

Can I call them "even tenths"?

For example:

"If the maximum value in the data set is 1, then the values displayed in the bar graph are the ______." I am pertaining to the numbers above.

0.2

0.4

0.6

0.8

Can I call them "even tenths"?

For example:

"If the maximum value in the data set is 1, then the values displayed in the bar graph are the ______." I am pertaining to the numbers above.

You can still ask an expert for help

asked 2022-07-19

complete k-partite graphs

I am trying to solve the following problem:

Let G be a nonempty graph with the property that whenever $uv\notin E(G)$ and $vw\notin E(G)$, then $uw\notin E(G)$. Prove that G has this property if and only if G is a complete k-partite graph for some $k\ge 2$. (Consider $\overline{G}$).

The converse is straightforward and is given by the definition of the complete k-partite graphs, however, the direct way is not trivial and I could not get it.

I am trying to solve the following problem:

Let G be a nonempty graph with the property that whenever $uv\notin E(G)$ and $vw\notin E(G)$, then $uw\notin E(G)$. Prove that G has this property if and only if G is a complete k-partite graph for some $k\ge 2$. (Consider $\overline{G}$).

The converse is straightforward and is given by the definition of the complete k-partite graphs, however, the direct way is not trivial and I could not get it.

asked 2022-08-27

One graph a subgraph of another?

Consider a graph G on n vertices with minimum degree $\delta $ and with its largest independent set $a>\delta $. Consider the graph ${\overline{K}}_{a}\otimes {K}_{n-a-1}$ (in other words, take a set of a points and add every edge relation between that set and ${K}_{n-a-1}$. Intuitively, this graph is a ${K}_{n-1}$ with a missing ${K}_{a}$).

How does one prove that that no matter how I take a vertex $v$ and connect it to $\delta $ vertices in the ${\overline{K}}_{a}$, I will always get a copy of G.

I think this is trivially true for bipartite graphs, but I dont know how to prove it in general. Any help is nice!

Consider a graph G on n vertices with minimum degree $\delta $ and with its largest independent set $a>\delta $. Consider the graph ${\overline{K}}_{a}\otimes {K}_{n-a-1}$ (in other words, take a set of a points and add every edge relation between that set and ${K}_{n-a-1}$. Intuitively, this graph is a ${K}_{n-1}$ with a missing ${K}_{a}$).

How does one prove that that no matter how I take a vertex $v$ and connect it to $\delta $ vertices in the ${\overline{K}}_{a}$, I will always get a copy of G.

I think this is trivially true for bipartite graphs, but I dont know how to prove it in general. Any help is nice!

asked 2022-08-12

Linear functions versus Logarithmic and Exponential functions

If a function is linear, I know that this should be true:

$f({x}_{2})-f({x}_{1})=f(\overline{x})$

Where $\overline{x}$ is the point exactly in between ${x}_{1}$ and ${x}_{2}$. Now, I know from looking at their graphs that the same shouldn't be true for logarithmic and exponential functions. That is, for logarithmic functions:

$f({x}_{2})-f({x}_{1})<f(\overline{x})$

And for exponential functions:

$f({x}_{2})-f({x}_{1})>f(\overline{x})$

I'm not a mathematician by formation, but I feel like it should be possible to prove this without having to look at their graph. Does anyone know how to do this?

If a function is linear, I know that this should be true:

$f({x}_{2})-f({x}_{1})=f(\overline{x})$

Where $\overline{x}$ is the point exactly in between ${x}_{1}$ and ${x}_{2}$. Now, I know from looking at their graphs that the same shouldn't be true for logarithmic and exponential functions. That is, for logarithmic functions:

$f({x}_{2})-f({x}_{1})<f(\overline{x})$

And for exponential functions:

$f({x}_{2})-f({x}_{1})>f(\overline{x})$

I'm not a mathematician by formation, but I feel like it should be possible to prove this without having to look at their graph. Does anyone know how to do this?

asked 2022-04-06

Is there a way to calculate the scale of the Y axis without values on the Y axis

given the following bar graph (which shows monthly revenue, but no actual values), is there a way to calculate the revenue (actual dollar amount) in 3/2013?

asked 2022-10-02

Strange math notation, vertical bar with parentheses.

So I was reading "Resistance Distance" (D. J. Klein, M. Randić) (Journal of Mathematical Chemistry 12(1993)81-95) when I came up with strange notation.

From the paper:

The graph adjacency matrix is defined as:

${A}_{xy}=(x|A|y)=\{\begin{array}{ll}1/{r}_{xy}& x\sim y\\ 0& \text{otherwise}\end{array}$

The graph degree matrix of a graph is defined as:

${\mathrm{\Delta}}_{xy}=(x|\mathrm{\Delta}|y)=\delta (x,y)\sum _{z}^{\sim x}1/{r}_{xy}$

$|\varphi )\equiv \sum _{x}|x)$

My main question is what does the combination of the vertical bar parentheses mean. Thanks in advance.

So I was reading "Resistance Distance" (D. J. Klein, M. Randić) (Journal of Mathematical Chemistry 12(1993)81-95) when I came up with strange notation.

From the paper:

The graph adjacency matrix is defined as:

${A}_{xy}=(x|A|y)=\{\begin{array}{ll}1/{r}_{xy}& x\sim y\\ 0& \text{otherwise}\end{array}$

The graph degree matrix of a graph is defined as:

${\mathrm{\Delta}}_{xy}=(x|\mathrm{\Delta}|y)=\delta (x,y)\sum _{z}^{\sim x}1/{r}_{xy}$

$|\varphi )\equiv \sum _{x}|x)$

My main question is what does the combination of the vertical bar parentheses mean. Thanks in advance.

asked 2022-07-16

Prove $\chi (G)\chi (\overline{G})\ge n$ for chromatic number of graph and its complement

Let us denote by χ(G) the chromatic number, which is the smallest number of colours needed to colour the graph G with n vertices. Let $\overline{G}$ be the complement of G. Show that

$\chi (G)+\chi (\overline{G})\le n+1$

$\chi (G)\chi (\overline{G})\ge n$

I was able to prove (a) using induction. Any hints on proving (b)?

Let us denote by χ(G) the chromatic number, which is the smallest number of colours needed to colour the graph G with n vertices. Let $\overline{G}$ be the complement of G. Show that

$\chi (G)+\chi (\overline{G})\le n+1$

$\chi (G)\chi (\overline{G})\ge n$

I was able to prove (a) using induction. Any hints on proving (b)?

asked 2022-08-27

Shift graph towards mean with time?

Say I have a bar graph with one dependent variable and one independent variable. Given a time t, I essentially want to modify the given graph so that as $t->\mathrm{\infty}$, all the bars become equal to the mean.

In other words, I essentially want to move the bars of the graph, so that the bars above the mean lower so that they are closer to it and bars below it rise so that they are also closer to it.

I would like to the transformation to happen in negative exponential time (In other words, the bars move a lot initially, and they only converge to the mean when after an infinite amount of time)

At any time, the mean value of the graph must be equal to the original mean.

Any ideas how I can do this? I've never really worked with statistics before.

Say I have a bar graph with one dependent variable and one independent variable. Given a time t, I essentially want to modify the given graph so that as $t->\mathrm{\infty}$, all the bars become equal to the mean.

In other words, I essentially want to move the bars of the graph, so that the bars above the mean lower so that they are closer to it and bars below it rise so that they are also closer to it.

I would like to the transformation to happen in negative exponential time (In other words, the bars move a lot initially, and they only converge to the mean when after an infinite amount of time)

At any time, the mean value of the graph must be equal to the original mean.

Any ideas how I can do this? I've never really worked with statistics before.