Abstract Let U(R,S) denote the class of all (0,1) m×n matrices having row sum vector R and column sum vector S. The interchange graph G(R,S) is the graph where the vertices are the matrices in U(R,S) and two...Abstract Let U(R,S) denote the class of all (0,1) m×n matrices having row sum vector R and column sum vector S. The interchange graph G(R,S) is the graph where the vertices are the matrices in U(R,S) and two vertices representing two such matrices are adjacent provided they differ by an interchange. It is proved that G(R,(1,1,...,1)) is a generalized Cartesian product of some Johnson Scheme graphs. Furthermore, its connectivity, diameter and transitivity (vertex ,edge ) are also determined.展开更多
文摘Abstract Let U(R,S) denote the class of all (0,1) m×n matrices having row sum vector R and column sum vector S. The interchange graph G(R,S) is the graph where the vertices are the matrices in U(R,S) and two vertices representing two such matrices are adjacent provided they differ by an interchange. It is proved that G(R,(1,1,...,1)) is a generalized Cartesian product of some Johnson Scheme graphs. Furthermore, its connectivity, diameter and transitivity (vertex ,edge ) are also determined.
