This mathematician's namesake transformation maps Q to "I minus Q times the inverse of quantity I plus Q" and can be used to parameterize orthogonal matrices as skew-symmetric matrices. This man names a color graph in which edges are labeled by generators. One result named for this mathematician can be shown by finding a bijection with the set of Prufer Sequences and is the special case of a theorem of Kirchoff which uses matrix cofactors. This man's namesake formula shows that there are "n to the power n minus 2" labeled trees on n vertices, and he co-names the theorem that a square matrix is a root of its own characteristic polynomial, along with Hamilton.  FTP, name this British mathematician, whose namesake theorem is that every group is isomorphic to a subgroup of the symmetric group 
This mathematician's namesake transformation maps Q to "I minus Q times the inverse of quantity I plus Q" and can be used to parameterize orthogonal matrices as skew-symmetric matrices. This man names a color graph in which edges are labeled by generators. One result named for this mathematician can be shown by finding a bijection with the set of Prufer Sequences and is the special case of a theorem of Kirchoff which uses matrix cofactors. This man's namesake formula shows that there are "n to the power n minus 2" labeled trees on n vertices, and he co-names the theorem that a square matrix is a root of its own characteristic polynomial, along with Hamilton.  FTP, name this British mathematician, whose namesake theorem is that every group is isomorphic to a subgroup of the symmetric group and who names a table showing the entire structure of a group
This mathematician's namesake transformation maps Q to "I minus Q times the inverse of quantity I plus Q" and can be used to parameterize orthogonal matrices as skew-symmetric matrices.
Arthur Cayley