1) Co)= C, and c (1)=[. $:‘I is a matrix of order n, whose entries I?!)= cij for i# j and I?(!’= 0 for all i.* I 2) C.‘(r)=[c:;‘]= c (G:)* r?(r), where the operation ‘I*” b the same as the ordinary row-by-column multiplication in matrix theory subject to the following rules: a) the operation I ‘+” satisfies the associative, commutative, and idempotent laws; b) the multiplication satisfies the associative and commutative laws, and e#? k= 0 for all k; c) the distributive law that ei (ej+ ek)=(e&j)+(e&k) holds; d) the element “0” has the properties that 0+ ek= ek and Oek= 0 for all k; and e) any term in~ $7’obtained by the above rules containing a term in any cf.:‘, s< r, as a factor is reduced to 0. The matrix C (r)=[E!;‘] is defined as~ 2:’= cl:’for i# j and C! T’= 0 for all i. I%

A Hamiltonian circuit of a finite graph G is a circuit* which passes through each vertex of G. A Hamiltonian path from vertex vi and vertex vi is a path2 from vi to vf which passes through all other vertices of G. A Hamiltonian center is a vertex which has at least one Hamiltonian path to each of the vertices of G. Because of their many practical applications, 111. PI the problem of determining the existence of Hamiltonian circuits, and Hamiltonian paths from one vertex to another has been attacked by many authors. Ill-141 However, there is no algorithm which can generate all the Hamiltonian circuits, Hamiltonian paths, and Hamiltonian centers of a graph simultaneously. The purpose of this correspondence is to present such an algorithm. This algorithm which is straightforward and applicable to both directed and undirected graphs, can easily be programmed on a digital computer.