Q3. Given an integer n > 0, construct a graph Pa such that the label of each vertex is a representation of a stack of n pancakes (e.g., for n = 7, one of the vertices has the label: 3,1,4,5,6,7,2, each digit indicating the size of a pancake in a stack of 7). In this graph, there is an edge between two vertices iff their labels can be obtained from each other with only one flip (e.g., label 3,1,4,5,6,7,2 and label 4,1,3,5,6,7,2 can be obtained from one another with a single flip after the third pancake from the top. So, there is an edge between these two vertices.) a. [5 pts) How many vertices does Pahave? b. [5 pts] What is the degree of each vertex of P..? c. [10 pts) How many edges does Pn have? d. [5 pts] For which values of n does Pia have an Euler circuit? e. [5 pts] What is the largest number of edges between two vertices of Pa