1. ### Graph from Adjacency Matrix

Denote the vertices of G G1, G2, G3, does the 2 in the matrix just means there's 2 paths of length 1 from G2 to G1? ie, look like this: thx
2. ### Minimum spanning tree recursive algorithm using only adjacency list

Looking for some help with starting points more so than solutions here. How can I go about proving 1, 2, and 3? I don't understand exactly what S is? Just an array of all e_{v} basically? Additionally I don't understand G vs. G_{S}? Design and analyze a minimum spanning tree recursive algorithm...

First note that my book uses the convention that for an adjacency matrix, say we have row i and column j where i = j, then the entry is twice the number of loops incident on i. In other words, if there is a loop on a vertex we put 2 as the matrix entry instead of 1. Now my book says "If A is...

Hi all; I need the proof of the folowing Theorem: If X is the adjacency matrix of a graph G with n vertices, and Y=X+X^2+X^3+....+X^{n-1}, then G is disconnected if and only if there exist at least one entry in matrix Y that is zero. Best Wishes

I am looking at some k-maps and puzzled about grouping the adjacent cells. Pretend this is a 4 variable k-map of F(A,B,C,D) (sorry, I don't know of a better way to display them): 1100 1001 1001 1100 I see 3 groups: 1100 1001 1001 1100 1100 1001 1001 1100 1100 1001 1001 1100 Are these 3...
6. ### how do I find number of vertices given adjacency matrix

If I am given the adjacency matrix \left[ {\begin{array}{ccccc} 0 & 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 0 \\ \end{array} } \right] then how do I find the number of vertices to determine if it's strongly connected? I guess this example could...