Two-point resistances and random walks on stellated regular graphs Academic Article

abstract

• 2019 IOP Publishing Ltd. A formula for computing the resistance between any two vertices in the stellated graph of a regular graph is obtained. It turns out that the two-point resistance of the stellated graph can be expressed in terms of the two-point resistance of the original graph. As a consequence, the Kirchhoff index (i.e. the sum of the effective resistances between all pairs of vertices) for the stellated graph is obtained, which extends the previously known result. The correspondence between random walks and electric networks is then used to obtain the mean first passage time and mean commute time for random walks on stellated graphs.

authors

• Klein, Douglas

published proceedings

• JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

altmetric score

• 2

author list (cited authors)

• Yang, Y., & Klein, D. J.

citation count

• 12

complete list of authors

• Yang, Yujun||Klein, Douglas J

publication date

• February 2019

publisher

• IOP Publishing  Publisher

published in

• Journal of Physics A: Mathematical and Theoretical  Journal

keywords

• Kirchhoff Index
• Mean Commute Time
• Mean First-passage Time
• Resistance
• Stellated Graph

Digital Object Identifier (DOI)

• 10.1088/1751-8121/aaf8e7

start page

• 075201

end page

• 075201

volume

• 52

issue

• 7

URL

• http://dx.doi.org/10.1088/1751-8121/aaf8e7