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Prove that every tree with two or more vertices is bichromatic?

Prove that the maximum vertex connectivity one can achieve with a graph G on n. 01. Define a bipartite graph. Prove that a graph is bipartite if and only if it contains no circuit of odd lengths. Define a cut-vertex. Prove that every connected graph with three or more vertices has at least two vertices that are not cut vertices. Prove that a connected planar graph with n vertices and e edges has e - n + 2 regions. 02. 03. 04. Define Euler graph. Prove that a connected graph G is an Euler graph if and only if all vertices of G are of even degree. Prove that every tree with two or more vertices is 2-chromatic. 05. 06. 07. Draw the two Kuratowski's graphs and state the properties common to these graphs. Define a Tree and prove that there is a unique path between every pair of vertices in a tree. If B is a circuit matrix of a connected graph G with e edge arid n vertices, prove that rank of B=e-n+1. 08. 09.


What is experiment in science?

It is a graph, chart, or pictures in a science project to prove that you did the project.


What is the difference between a distance vs time graph and a distance vs time square graph?

The x axis has a different scale dist vs time: y axis is distance, x axis is time 1,2,3,4 etc equally spaced. dist vs time squared: y is still distance, but x is 1, 4, 9, 16 etc equally spaced. theat means the distance from 1 to 4 is the same as the distance from 4 to 9 and is the same from 9 to 16 etc. Some date graphed on the first might be a curve, but the advantage of the second is that the graph might then be a straight line, this technique is usually used to prove that equation should be using t2


What does the horizontal line test prove?

I posted this question myself to be honest because i wasn't sure... but the horizontal line test was made to prove whether the function/graph was an one-to-one function


What is the definition of line graph?

is a graph;that is used to jock down data.(uses dots and connects lines to it)


If you traveled five hundred years into the past and with nothing from this time could you prove you were from this time?

To prove something you need proof, and proof is defined as ,"any factual evidence that helps to establish the truth of something", and evidence is an actual visual thing, and if you have NOTHING that is visual of and actual object, you cannot prove it, so no.


How would you prove in general that the midpoint formula actually gives you the midpoint?

94 to be exact


Prove Hall's theorem from Tutte' theorem graph theory?

in this theorem we will neglect the given resistance and in next step mean as second step we will solve


What did Albert Einstien discover?

Albert Einstien discovered a refrigerator that ran without electricity! He was also the one to prove that nothing traveled faster than the speed of light.


How can you prove that food gives energy?

It's quite simple too prove that food gives you energy. If you never ate for days apart you would be very rundown and tired. So the answer to the question is basically the way to prove that food gives you energy is try not eat it and be energetic.


How do you prove graphically that a reaction is first order?

To prove graphically that a reaction is first order, you would plot the natural log of the concentration of the reactant versus time. If the resulting graph is linear, then the reaction is first order. This linear relationship indicates that the rate of the reaction is directly proportional to the concentration of the reactant.


Prove that a graph G is connected and only if it has a spanning tree?

Proving this is simple. First, you prove that G has a spanning tree, it is connected, which is pretty obvious - a spanning tree itself is already a connected graph on the vertex set V(G), thus G which contains it as a spanning sub graph is obviously also connected. Second, you prove that if G is connected, it has a spanning tree. If G is a tree itself, then it must "contain" a spanning tree. If G is connected and not a tree, then it must have at least one cycle. I don't know if you know this or not, but there is a theorem stating that an edge is a cut-edge if and only if it is on no cycle (a cut-edge is an edge such that if you take it out, the graph becomes disconnected). Thus, you can just keep taking out edges from cycles in G until all that is left are cut-gees. Since you did not take out any cut-edges, the graph is still connected; since all that is left are cut-edges, there are no cycles. A connected graph with no cycles is a tree. Thus, G contains a spanning tree. Therefore, a graph G is connected if and only if it has a spanning tree!