Unity – How can I achieve a plexus effect with VFX Graph?

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topological graph theory – thickness of the space cover

A book embedment of a graph G consists of placing the vertices of G on a ridge and assigning edges of the graph to sides so that edges on the same side do not intersect. The page number is a measure of the quality of a book embed, which is the minimum number of pages in which the graph G can be embedded.

Is a graph $ G $ is a diagram overlapping chart $ B $.
Is there a relationship between their page number?

I think the covering diagram is more complicated than the basic diagram. So too $ pn (G) geq pn (B) $ generally hold?

Graph theory – online algorithm for finding clique of size k

I'm trying to write an online algorithm that can detect k size cliques. I start with a series of vertices first. For each iteration, I add an edge. The algorithm recognizes the first time that an edge generates a clique of size k. What is an efficient algorithm that can accomplish this task, and what is the temporal complexity?

Graph two lines in Google Sheets based on the values ​​in the first column

I am trying to create two lines in the same diagram, where a "line A" is based on data named "A" and "line B" based on B.

The x-axis is the date and will be extended over time as more entries are added. The weight would be the Y-axis.

I can not seem to convince Google Sheets to divide the data into two lines based on the "Name" column. Any help would be appreciated. πŸ™‚

An example of data that I want to plot graphically with two lines

randomized algorithms – how can the maximum number of minimum slices of a graph choose exactly $ n 2 $?

After my teacher, $ n choose $ 2 is the maximum number of minimum cuts that we can have in a graph. To prove this, he showed the lower limit with an n-cycle diagram. To prove the upper bound, he subtracted the argument from two facts:

  • Probability of finding $ i ^ {th} $ min $ geq frac {2} {n (n-1)} = frac {1} {n choose 2} $
  • Event of finding $ i ^ {th} $ Min cut is disjoint.

So he simply added the probabilities for which he had proven the upper limit $ n choose $ 2,

Now consider a tree as a graph $ n $ Knots, then we can close $ (n-1) $ min cuts that are less than $ n choose $ 2 Cuts ($ n geq3) $, Do I miss something here?

Graph theory – Determination of the dependence of the maximum vertex degree on the k-dyeability

How do we describe a construction of a two-color graph in which the degree of each vertex is greater than or equal to (| V | -1) / 2? What can be said on this basis about the dependence of the maximum vertex degree on the k-dyeability of a graph?

My first thought is that one vertex to connect to every other vertex in a graph, | V | -1 must be. However, considering half of them in (| V | -1) / 2, this would only be related to half of the vertices in the graph. So if this were the case for all vertices in G, we would construct a 2-color bipartite graph (that's my idea).

However, I am not sure how to handle the second part. I know that in a graph there can be n different colors for k given vertices in a row, and we have to add colors if there are adjacent vertices, but I can not figure out how the maximum vertex degree affects the number in particular Colors that we can use for a diagram.

Draw – Insert multiple lines at specified locations on a 3D graph

data = table[{x, y, Cos[x] sin[y]}, {x, 0, Ο€, 0,1}, {y, 0, 2 Ο€, 0,2}];

Lines = Graphics3D[{Red, Thick, Line[{{Pi, #, -1}, {Pi, #, 1}}] & / @ {2, 3, 5}}];
show[ListPlot3D[Flatten[data, 1]], Lines]

Enter image description here

Alternatively you can use Face grids and Face Grid Style:

ListPlot3D[Flatten[data, 1].
FaceGrids -> {{{1, 0, 0}, {{2, 3, 5}, {}}},
FaceGridsStyle -> directive[Red, Thick]]

Graph theory – Helly vs. Strong Helly property of hypergraphs

I'm not clear about the difference between Helly and Strong Helly's property. For example, hypergraph
H (V, E), V = {1,2,3} and E = {(1,2), (2,3), (1,3)}
There is a non-empty sentence for each cross-over pair, which classifies it as Helly (but not strong Helly). However, this triangle hypergraph is not considered a helly hypergraph. Insights and corrections are welcome.

Algorithms – Shortest path in an incomplete graph

Algorithms do not care if you find out which edges extend from a vertex by looking up them in an array by calling a called function receive() or by waiting for divine revelation.

The only problem with the Dijkstra algorithm is that, as usually described, it first sets the range estimate for each node to infinity and adds each node to a queue. You can not do this if you do not know the nodes at the beginning of the algorithm. But Dijkstra does not have to do that, and even knowing the chart before you start does not make it very efficient. It's enough to add the nodes to the queue when you discover them. This variant of the algorithm is often referred to as a "uniform cost search" (especially in AI), although some people argue that it is only the Dijkstra algorithm and that Dijkstra never Really This will add all nodes at the beginning of the queue.

If you look at the two algorithms / versions of the algorithm, you will notice that a node that the classic Dijkstra considers to be infinite is a node that has not yet been queued at uniform cost.

Ariel Felner gave a good analysis of the relationship between classic disjkstra and uniform-cost Dijkstra's Algorithm versus Uniform Cost Search or a Case Against Disjkstra's Algorithm (Proc. 4th Intl. Symposium on combinatorial search (SoCS 2011)AAAI Press, 2011; PDF).

Why can not I authenticate using Microsoft Graph Explorer through the custom SharePoint Web Part only in the Edge Browser?

I have deployed a custom Web Part on Sharepoint Online where I authenticate to Microsoft Graph Explorer.

It is successfully authenticated through the custom Sharepoint Web Part in chrome. IE and Feuerfuchs but not authenticated in Edge.

In Edge I get the following error:

Enter image description here

description: "Invalid argument"
message: "Invalid argument"
Number: -2147418113
stack: "TypeError: Invalid argument on anonymous function (https://spoprod-a.akamaihd.net/files/sp-client-prod_2019-05-31.012/sp-pages-assembly_en-us_80b161431b1b8ce356b58dd5ab1df0cc.js:1178:42819)

This is my method, and I've found that the API provides the answer in Chrome, IE, and Firefox at the time of calling the Microsoft Graph Explorer API (https://graph.microsoft.com), but in Edge "catch" part and throwing mistakes.

private _getListApplications (param): promise {
return this.context.aadHttpClientFactory.getClient (& # 39; https: //graph.microsoft.com')
.then ((client: AadHttpClient) => {
return client.get ("https://graph.microsoft.com/beta/applications", AadHttpClient.configurations.v1);
}). then ((responseListAllApps: SPHttpClientResponse) => {
return responseListAllApps.json ();
}). catch (err => {console.log (# errr # 39 ;, err);});