For the following problems, answer yes or no and provide proof and explanation for your answer.

$1.)$ If the graph non$-$isomorphism problem does not have a polynomial time solution, then P $$ NP

$2.)$ If the graph isomorphism problem has a polynomial$-$time solution, then P $=$ NP

$3.)$ If the fastest running time to solve the question of whether a collection of clauses does not have a satisfying assignment is at least n$^($log n$),$ then P $$ NP

$4.)$ If the Euler Path problem is in NPC$,$ then P $=$ NP