Let G_1 and G_2 be vertex-disjoint graphs with n_1 and n_2 vertices,m_1 and m_2 edges,respectively.The corona G_1° G_2 of G_1and G_2 was defined as the graph obtained by taking one copy of G_1and n_1 copies of G_...Let G_1 and G_2 be vertex-disjoint graphs with n_1 and n_2 vertices,m_1 and m_2 edges,respectively.The corona G_1° G_2 of G_1and G_2 was defined as the graph obtained by taking one copy of G_1and n_1 copies of G_2,and then joining the ith vertex of G_1 to every vertex in the ith copy of G_2.The edge corona G_1° G_2 of G_1 and G_2was defined as the graph obtained by taking one copy of G_1 and m_1copies of G_2,and then joining two end-vertices of the ith edge of G_1to every vertex in the ith copy of G_2.Kirchhoff index of G_1 ° G_2 was obtained in a much simple proof and the resistance distance of G_1 °G_2 is obtained.Furthermore,the Kirchhoff index and the resistance distance of G_1 ° G_2 were obtained.展开更多
基金National Natural Science Foundation of China(No.11461020)the Youth Foundation of Hexi University in Gansu Province,China(No.QN2013-07)the Teaching Reform Project of Hexi University,China(No.HXXXJY-2014-011)
文摘Let G_1 and G_2 be vertex-disjoint graphs with n_1 and n_2 vertices,m_1 and m_2 edges,respectively.The corona G_1° G_2 of G_1and G_2 was defined as the graph obtained by taking one copy of G_1and n_1 copies of G_2,and then joining the ith vertex of G_1 to every vertex in the ith copy of G_2.The edge corona G_1° G_2 of G_1 and G_2was defined as the graph obtained by taking one copy of G_1 and m_1copies of G_2,and then joining two end-vertices of the ith edge of G_1to every vertex in the ith copy of G_2.Kirchhoff index of G_1 ° G_2 was obtained in a much simple proof and the resistance distance of G_1 °G_2 is obtained.Furthermore,the Kirchhoff index and the resistance distance of G_1 ° G_2 were obtained.
