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Graphs with disjoint dominating and paired-dominating sets

100%

Southey J. , Henning M.

Open Mathematics

2010

tom 8

nr 3

459-467

A dominating set of a graph is a set of vertices such that every vertex not in the set is adjacent to a vertex in the set, while a paired-dominating set of a graph is a dominating set such that the subgraph induced by the dominating set contains a perfect matching. In this paper, we show that no minimum degree is sufficient to guarantee the existence of a disjoint dominating set and a paired-dominating set. However, we prove that the vertex set of every cubic graph can be partitioned into a dominating set and a paired-dominating set.

Amazonian Corruption Problems in the Education System in the Light of Sustainable Development

75%

Alves I. M. , de São Pedro Filho F. , Kowal J.

International Journal of Pedagogy, Innovation and New Technologies

2022

tom 9(2)

43-59

Corruption is a social phenomenon that has existed since the beginning in all communities, present in everyday situations, and affects the education system. We reviewed the various aspects of corruption in the Amazon education system basing on domination theory. We looked for factors that facilitate corruption in the education system and harm sustainable development in the Amazon. We have also shown the relationships between domination theory, scientific knowledge degradation, and sustainable development. We have identified some options to fight corruption in the education system to ensure sustainable development in the Amazon. We have implemented a qualitative research project under the Amazon Graduate Program to reach described goals. Our research methods included critical literature analysis, case study, direct observation, and content analysis to describe the literature review concepts. Through the Ishikawa diagram's graphic representation, we highlighted the causes of traditional domination and corruption sub-causes that cause the degradation of scientific knowledge and sustainability in the Amazon. The study concludes that the domination in the education system is similar to traditional domination. Corrupt actions can be decisive for preventing the construction of knowledge about Sustainability in the Amazon. The scenario warns of a crisis in the education system. Our findings allow us to suggest significant actions for coping with curbing corrupt practices and unethical actions in the system. Our Amazonian academy findings help reflect the reality of the managers and politicians sensitized with this investigative work.