论文信息 - Group inverse of the Laplacian of connections of networks

Group inverse of the Laplacian of connections of networks

In previous works the group inverse of a network obtained by some perturbations, as the deletion of a vertex, the addition of a new vertex, contraction of an edge, etc. is obtained in terms of the group inverse of the original network. In this work, two given networks are connected with some new edges and the group inverse of the new network is related with the group inverses of the two original networks. In particular, the formula for the connection of two networks by just one edge is obtained, and besides the formula for the Kirchhoff index of this kind of network.

S. Gago

[1] S. Gago,et al. Green operators of networks with a new vertex , 2015 .

[2] Douglas J. Klein,et al. Resistance distances in composite graphs , 2014 .

[3] Margarida Mitjana,et al. Discrete elliptic operators and their Green operators , 2014 .

[4] Enrique Bendito,et al. The Kirchhoff indices of join networks , 2012, Discret. Appl. Math..

[5] Margarida Mitjana,et al. Kirchhoff Indexes of a network , 2010 .

[6] Yanfeng Luo,et al. The Laplacian polynomial and Kirchhoff index of graphs derived from regular graphs , 2013, Discret. Appl. Math..

[7] Heping Zhang,et al. Kirchhoff index of composite graphs , 2009, Discret. Appl. Math..

[8] Adi Ben-Israel,et al. Generalized inverses: theory and applications , 1974 .

[9] Zubeyir Cinkir. Deletion and contraction identities for the resistance values and the Kirchhoff index , 2011 .

[10] Margarida Mitjana,et al. The inverses of some circulant matrices , 2015, Appl. Math. Comput..

[11] Douglas J. Klein,et al. A recursion formula for resistance distances and its applications , 2013, Discret. Appl. Math..

[12] S. R. Simanca,et al. On Circulant Matrices , 2012 .

[13] Ching-hsiang Hung,et al. The Moore-Penrose inverse of a partitioned matrix ? , 1975 .

[14] F. Spieksma,et al. Effective graph resistance , 2011 .