【摘要】 设G1和G2是两个连通图,则G1和G2的Kronecker积G1×C2定义如下:V(G1×G2)=V(G1)×V(G2),E(G1×G2)={(u1,v1)(u2,v2):u1u2∈E(G1),v1v2∈E(G2)}.该文证明了如果G=G1×G2是平面图并且︱Gi︱≥3,那么G1和G2都是平面图;还完全确定了Pn×G2的平面性,n=3,4.更多还原

【Abstract】 Let G1and G2be two connected graphs.The Kronecker product G1×G2is the graph with vertex set V(G1×G2)=V(G1)×V(G2)and the edge set E(G1×G2)={(u1,v1)(u2,v2)∶u1u2∈E(G1),v1v2∈E(G2)}.We consider the planarity of G1×G2.In particular,we totally determine that when Pn×G2is plallar,n=2,3.更多还原