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An infinite family of 2-connected graphs that have reliability factorisations

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journal contribution
posted on 2017-02-19, 00:00 authored by Kerri Morgan, R Chen
The reliability polynomial Π(G,p) gives the probability that a graph is connected given each edge may fail independently with probability 1−p. Two graphs are reliability equivalent if they have the same reliability polynomial. It is well-known that the reliability polynomial can factorise into the reliability polynomials of the blocks of a graph. We give an infinite family of graphs that have no cutvertex but factorise into reliability polynomials of graphs of smaller order.

Brown and Colbourn commented that it was not known if there exist pairs of reliability equivalent graphs with different chromatic numbers. We show that there are infinitely many pairs of reliability equivalent graphs where one graph in each pair has chromatic number 3 and the other graph has chromatic number 4.

History

Journal

Discrete applied mathematics

Volume

218

Pagination

123 - 127

Publisher

Elsevier

Location

Amsterdam, The Netherlands

ISSN

0166-218X

eISSN

1872-6771

Language

eng

Publication classification

C Journal article; C1.1 Refereed article in a scholarly journal

Copyright notice

2016, Elsevier B.V.