(Solved): Suppose G is a graph with vertices a,b,c,d,e,f with adjacency matrix 010100100111000011 ...

Suppose $$\mathrm{G}$$ is a graph with vertices $$a,b,c,d,e,f$$ with adjacency matrix $$\left(\begin{array}{llllll}0& 1& 0& 1& 0& 0\\ 1& 0& 0& 1& 1& 1\\ 0& 0& 0& 0& 1& 1\\ 1& 1& 0& 0& 1& 0\\ 0& 1& 1& 1& 0& 1\\ 0& 1& 1& 0& 1& 0\end{array}\right)$$ Find: a. the number of vertices in $$G$$. b. the number of edges in $$\mathrm{G}$$. c. the degree of each vertex. d. the number of loops. e. the length of the longest simple path in $$\mathrm{G}$$. f. the number of components in $$\mathrm{G}$$. g. the distance between vertex a and vertex c.