Disjunctive Total Domination in Graphs

Let $G$ be a graph with no isolated vertex. In this paper, we study a parameter that is a relaxation of arguably the most important domination parameter, namely the total domination number, $\gamma_t(G)$. A set $S$ of vertices in $G$ is a disjunctive total dominating set of $G$ if every vertex is adjacent to a vertex of $S$ or has at least two vertices in $S$ at distance2 from it. The disjunctive total domination number, $\gamma^d_t(G)$, is the minimum cardinality of such a set. We observe that $\gamma^d_t(G) \le \gamma_t(G)$. We prove that if $G$ is a connected graph of order$n \ge 8$, then $\gamma^d_t(G) \le 2(n-1)/3$ and we characterize the extremal graphs. It is known that if $G$ is a connected claw-free graph of order$n$, then $\gamma_t(G) \le 2n/3$ and this upper bound is tight for arbitrarily large$n$. We show this upper bound can be improved significantly for the disjunctive total domination number. We show that if $G$ is a connected claw-free graph of order$n > 10$, then $\gamma^d_t(G) \le 4n/7$ and we characterize the graphs achieving equality in this bound.Comment: 23 page

The digital repository as a central driver in the open access research agenda

[From introduction] The Berlin Declaration was drafted to “promote the Internet as a functional instrument for a global scientific knowledge base and human reflection”, and has played a significant role in advancing open access to research and scholarly material. This declaration has been signed by over 250 organisations from all over the world. In line with the above, the Digital Repository, has emerged as a dynamic platform for promoting “scientific knowledge and human reflection”. It plays a significant role in promoting the research output of an institution within the Open Access arena.Poster presented at the World Library and Information Congress (WLIC) in Cape Town, 15 -21 August 2015

Graphs with Large Disjunctive Total Domination Number

Let $G$ be a graph with no isolated vertex. In this paper, we study a parameter that is a relaxation of arguably the most important domination parameter, namely the total domination number, $\gamma_t(G)$. A set $S$ of vertices in $G$ is a disjunctive total dominating set of $G$ if every vertex is adjacent to a vertex of $S$ or has at least two vertices in $S$ at distance $2$ from it. The disjunctive total domination number, $\gamma^d_t(G)$, is the minimum cardinality of such a set. We observe that $\gamma^d_t(G) \le \gamma_t(G)$. Let $G$ be a connected graph on $n$ vertices with minimum degree $\delta$. It is known [J. Graph Theory 35 (2000), 21--45] that if $\delta \ge 2$ and $n \ge 11$, then $\gamma_t(G) \le 4n/7$. Further [J. Graph Theory 46 (2004), 207--210] if $\delta \ge 3$, then $\gamma_t(G) \le n/2$. We prove that if $\delta \ge 2$ and $n \ge 8$, then $\gamma^d_t(G) \le n/2$ and we characterize the extremal graphs.Comment: 50 page

Barriers to tacit knowledge retention: an understanding of the perceptions of the knowledge management of people inside and outside the organisation

BACKGROUND: Knowledge loss causes challenges for organisations that wish to remain competitive. These organisations must identify the risks that could lead to knowledge loss and become aware of issues that affect knowledge retention. OBJECTIVES: The objective of this research was to identify tacit knowledge retention barriers that could cause knowledge loss in an organisation. The paper presents a framework for the assessment of the impact of these barriers and discusses the research findings in order to critique that framework. METHOD: A quantitative strategy was used to interpret the findings. The target population is information technology (IT) professionals in a government organisation. Interviews were conducted in order to produce a more context-sensitive interpretation of the findings. A quantitative research approach was used to ensure the findings would precisely reflect the target population. RESULTS: The majority of respondents confirmed that career development requires professional development, training prospects and improves the employability of employees. The agreed result was that respondents seek autonomy, that is, the ability to make decisions. Job stress and burnout are experienced because of problems with in filling posts, and the competition between the private and public sectors for experienced IT employees. CONCLUSION: Certain determinants were found that affect barriers in knowledge management: organisational commitment, job satisfaction, job characteristics and talent management. These need to be measured to prevent barriers from occurring. Implications are drawn from the study; these provide a focus for further research to bridge some gaps in information technology that currently limit the widespread use of knowledge management.Department of HE and Training approved lis

A cross-sectional analytical study of geophagia practices and blood metal concentrations in pregnant women in Johannesburg, South Africa

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