ORCID Profile
0000-0002-5965-9825
Current Organisations
La Trobe University
,
Shiraz University
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Publisher: Springer Science and Business Media LLC
Date: 11-05-2022
Publisher: Elsevier BV
Date: 09-2020
Publisher: Wiley
Date: 28-12-2022
DOI: 10.1002/JGT.22923
Abstract: A vertex coloring of a graph is called distinguishing if no nonidentity automorphisms of can preserve it. The distinguishing number of , denoted by , is the minimum number of colors required for such a coloring, and the distinguishing threshold of , denoted by , is the minimum number such that every ‐coloring of is distinguishing. As an alternative definition, is one more than the maximum number of cycles in the cycle decomposition of automorphisms of . In this paper, we characterize when is disconnected. Afterwards, we prove that, although for every positive integer there are infinitely many graphs whose distinguishing thresholds are equal to , we have if and only if . Moreover, we show that if , then either is isomorphic to one of the four graphs on three vertices or it is of order , where is a prime number. Furthermore, we prove that if and only if is asymmetric, or . Finally, we consider all generalized Johnson graphs, , which are the graphs on all ‐subsets of where two vertices and are adjacent if . After studying their automorphism groups and distinguishing numbers, we calculate their distinguishing thresholds as , unless and in which case we have .
Publisher: MDPI AG
Date: 14-07-2022
DOI: 10.3390/LAWS11040056
Abstract: Australian trans youth seeking medical treatment for gender dysphoria can encounter significant legal barriers to healthcare. Legal requirements for obtaining valid consent to gender-affirming care, first established in 2004, mean that an application to the Family Court is required in many cases before treatment can be provided. The development of Australian law concerning consent for the medical treatment of trans youth has been slow, haphazard, and remains incomplete. The Family Court process has been found to be damaging to trans youth and their families. There is widespread agreement that the law needs reform, even more so since the 2020 decision in Re: Imogen. This article explores the implications of the decision in Re: Imogen for trans youth and their families and raises possible models for reform. It starts by providing the background to Re: Imogen and explaining the current legal position. It then explores why the law needs to be reformed, highlighting the inconsistent approach to competency in Australian law and the harm the current law does to trans youth. Building on critiques of the law in this area, it reviews various options for law reform and suggests an optimal model.
No related grants have been discovered for Fiona Kelly.