MAT 419 SOLUTION

Q1a.
                                                                   SOLUTION

from the format of the matrix we can get our 7×7 adjacency matrix using this format: 
│ a11 a12 a13 a14 a15 a16 a17│
│ a21 a22 a23 a24 a25 a26 a27│
│ a31 a32 a33 a34 a35 a36 a37│
│ a41 a42 a43 a44 a45 a46 a47│
│ a51 a52 a53 a54 a55 a56 a57│
│ a61 a62 a63 a64 a65 a66 a67│
│ a71 a72 a73 a74 a75 a76 a77│

Therefore:

            │ 2  0  1  0  1  0  1│
            │ 0  2  0  0  1  0  0│
            │ 1  0  2  0  1  0  1│
A(G)= │ 0  0  0  2  0  0  0│
            │ 1  1  1  0  2  0  1│
            │ 0  0  0  0  0  2  0│
            │ 1  0  1  0   1 0  2│

Q1b. Then C(v) is nothing but component of the graph. Then: C(v) = 3
then as you can see that we have two isolated vertices from our graph form by the above adjacency matrix which are V6 and V4 therefore V6 is a cut-vertex and V4 is also a cut-vertex while V1,V2,V3,V5 and V7 are vertex-cut.
 
Q2,Q3 and Q4 very soon by God will