整可逆图的克罗内克积的逆

Inverse of Kronecker product of integrally invertible graphs

图G_(1)和G_(2)的克罗内克积G_(1)■G_(2)具有点集V(G_(1))■V(G_(2)),在G_(1)■G_(2)中两个点(u_(1),v_(1))和(u_(2),v_(2))相邻当且仅当u_(1)u_(2)∈E(G_(1))且v_(1)v_(2)∈E(G_(2))。对整可逆图(即图的邻接矩阵的逆矩阵中只包含整数)的克罗内克积的逆进行刻画。

The Kronecker product G_(1)■G_(2) of graphs G_(1) and G_(2) is the graph with the vertex set V(G_(1))■V(G_(2)), two vertices(u_(1),v_(1)) and(u_(2),v_(2)) being adjacent in G_(1)■G_(2) if and only if u_(1)u_(2)∈E(G_(1)) and v_(1)v_(2)∈E(G_(2)). The inverse of Kronecker product of integrally invertible graph is characterized.