Im currently confused and need help with this homework . I have no idea where to start ; if anyone can help me with these 6 problems and explain it to me. I would really appreciate it.

This is Graph Theory if your confused as well

1. Let G be a simple graph and all edges are assigned a length 1. A geodesic is a path, a) Show that if u = tovi vk-u is a geodesic G than vi vi+1 y is also a geodesic for b) Let G be a graph in which the distance between any two vertices is odd. Show that 2. Let in the complete graph of 17 vertices all edges are colored in 3 colors. Show that 3. (Problem 39 from Chapter 1, Exercises) How many graphs isomorphic to C4 are 4. ( Problem 28 from Chapter 1, Exercises) Show that any degree sequence of a non- 5. Show that in a complete graph with 6 vertices and edges colored in 2 colors, there which realizes the shortest distance between two points. this is the complete graph there is a single-colored triangle. there in Km,n trivial graph has two equal terms. are at least 2 single-colored triangles. 6. A K3 subgraph of a graph G is called a 3-clique (or triangle). Let G be a graph with 3-cliques C1,.., Ck and vertices v1, ..., Up. A 3-clique incidence matrix A is a matrix with n rows and p columns, which has entries aij = 1 or aij = 0 depending on whether vi e C. pr viCi respectively. If Ar is the transposed matrix-where i-th row becomes i-th column and vice versa, then explain what the entries of AAT mean for the graph G. Note the difference between the diagonal and the off-diagonal ones