Resistance distances in composite graphs Academic Article

abstract

• 2014 IOP Publishing Ltd. The resistance distance between any two vertices of a connected graph is defined as the effective resistance between them in the electrical network constructed from the graph by replacing each edge with a (unit) resistor. Let G + H, G x H, G[H], G H, G x H, GH and G{H} be the join, product, composition, direct product, strong product, corona and rooted product of two graphs G and H, respectively. In this paper, formulae for resistance distances of these composite graphs are given in terms of parameters of the parent graphs, and some properties are established. Explicit formulae are obtained for resistance distances of some classes of graphs, including rook graphs, diagonal mesh graphs and generalized double graphs.

authors

• Klein, Douglas

published proceedings

• JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

author list (cited authors)

• Yang, Y., & Klein, D. J.

citation count

• 12

complete list of authors

• Yang, Yujun||Klein, Douglas J

publication date

• September 2014

publisher

• IOP Publishing  Publisher

published in

• Journal of Physics A: Mathematical and Theoretical  Journal

keywords

• Algebraic Connectivity
• Composite Graph
• Laplacian Spectrum
• Rayleigh's Short-cut Principle
• Resistance Distance

Digital Object Identifier (DOI)

• 10.1088/1751-8113/47/37/375203

start page

• 375203

end page

• 375203

volume

• 47

issue

• 37

URL

• http://dx.doi.org/10.1088/1751-8113/47/37/375203