Give a formal encoding of directed graphs as binary strings using an adjacencymatrix representation. Do the same using an adjacency-list representation. Argue that the two representations are polynomially related.

Give a linear time algorithm via pseudo code that takes as input a directed acyclic graph G (V, E) and two vertices u and v, that returns the number of simple paths from u to v in G. Your algorithm needs only to count the simple paths, not list them. Explain why your code runs in linear time.

please send correct answer for part a

The problem Monochomatic-Subgraph-Avoidance takes as input two undirected graphs Fand G. It asks where F can be colored with two colors (say, red and blue) that does not containa monochomatic (all-red or all-blue) G as a subgraph. (Note that when G has two nodes and oneedge between them, this is equivalent to the 2-coloring problem of asking whether F can be coloredso that no neighbors have the same color.)Next, show that Monochomatic-Subgraph-Avoidance is contained in one of the classes inthe second level of the polynomial hierarchy.  ALso provide an expression using qualifiers. YOU ALSO NEED TO PROVIDE A CLEAR EXPRESSION USING THE QUALIFIERS.PLEASE GIVE CLEAR EXPLAINATION.