3. Knnn be a complete 3-bipartite graph whose maximal independent sets are C1 = [n],C2 = [20] - [n), and C3 = 3n] - [2n). (a) How many edges does Kn, have? (b) Does Kn,n,n have an Eulerian cycle? (c) Show by any means that K... has a Hamilton cycle. (d) Let G be the graph that is obtained from Kn,n,ne by removing the edges of your Hamilton cycle.

(c) The number of triangles T present in the network, where a triangle means three nodes, each connected by links to the other two (Hint: you can use the trace of a matrix) (d) The vector knn whose element j is the sum of the degrees of node i's neighbors. (e) The vector knnn whose element i is the sum of the degrees of node i's second neighbors.

Let A be the NxN adjacency matrix of an undirected unweighted network, without self-loops. Let 1 be a column vector of N elements, all equal to