Basics in graph theory

The content here is same as the wikipedia entry at this link. I am just writing this as i can't seem to concentrate by just reading.

Complete graph - all possible pairs of vertices are adjacent or the degree of all vertices is |V|-1.
k-regular graph - every node in a graph with n nodes has the same degree k<= n-1.
Line graph - the line graph of G, denoted as L(G),  is the graph where the edges of G correspond to the nodes of L(G), and  two edges in L(G)  are adjacent if they share a node in G.

The adjacency matrix - The adjacency matrix A(X) of a directed graph X is the integer matrix with roes and columns indexed by the vertices of X,  such that the uv-entry if A(X) is equal to the number arcs FROM u TO v.
The spectrum of graph X is the set of eigen values  of A(X) along with their multiplicities.


Cycles are of two types.
1. Closed walk - sequence of vertices starting and ending at the same vertex. Its implied that the vertices are adjacent  to each other.
2. Simple cycle - closed walk with no repetition of vertices or edges allowed, other than the starting vertex.

Tree - is an undirected graph in which any two vertices are connected by a simple path.
Spanning tree - The spanning tree of a connected undirected graph G is a tree that includes all the vertices and some or all of the edges of G.

Vector spaces defined on a graph - vertex space, edge space, cycle space, cut space.

My Movie playlist

There are some movies that I keep watching over and over. some of them are,
1. Revolver(2005)
2. V for vendetta(2005)
3. MindGame(2004) (Japanese)
4. Pi(1998)
5. Waking Life(2001)
5. My fair Lady(1964)
6. Monty Python and the holy grail(1975)

Have got a new list of movies from my friends. hopefully will update this soon.

Exporting simulink model as a image

in the command window,
>> orient('myModel','portrait'); % can use landscape. based on the model
>> print -dpng -r300 -smyModel filename.png

done.

Debugging the DSO board

Our DSO board arrived. We are using two Atxmegas. One for ADC and USB communication. The other for waveform generation.
Now, for some reason the input at PA1(input to ADC) is giving us problems. The external input is scaled and shifted using opamps and then given to ADC pins. i.e., PORTA. This is so that the pins of the controller are not given voltages outside the absolute voltage specifications (-0.5V to 3.3V).

28 feb -
found out that PA0, 3.3V and ground volt were shorted.
i was "being stupid".
There was no short. Amaldev had to come all the way from his lab to verify that.
One day, he is gonna snap and throw  me in front of a running bus.

Anyways, on burning the final code we had written, the voltages at PA1 and PA2 are getting stuck at 2.1V.
On burning our earlier ADC codes, there is no problem.

Resolved. In a file included by the example project, on which our entire project stands on.