On Average Distance of Neighborhood Graphs and Its Applications

Graph invariants such as distance have a wide application in life, in particular when networks represent scenarios in form of either a bipartite or non-bipartite graph. Average distance μ of a graph G is one of the well-studied graph invariants. The graph invariants are often used in studying efficiency and stability of networks. However, the concept of average distance in a neighborhood graph G′ and its application has been less studied. In this chapter, we have studied properties of neighborhood graph and its invariants and deduced propositions and proofs to compare radius and average distance measures between G and G′. Our results show that if G is a connected bipartite graph and G′ its neighborhood, then radG1′≤radG and radG2′≤radG whenever G1′ and G2′ are components of G′. In addition, we showed that radG′≤radG for all r≥1 whenever G is a connected non-bipartite graph and G′ its neighborhood. Further, we also proved that if G is a connected graph and G′ its neighborhood, then and μG1′≤μG and μG2′≤μG whenever G1′ and G2′ are components of G′. In order to make our claims substantial and determine graphs for which the bounds are best possible, we performed some experiments in MATLAB software. Simulation results agree very well with the propositions and proofs. Finally, we have described how our results may be applied in socio-epidemiology and ecology and then concluded with other proposed further research questions

Participation of female students in undergraduate Mathematics at the University of Malawi

International audienc

Participation of female students in undergraduate Mathematics at the University of Malawi

International audienc

Investigating human-induced threat to hydrological regime of Lake Chilwa Basin, Malawi

Abstract The sensitivity of watersheds to climatic and land use alterations remains subject of scientific interest globally. In this study, we analysed hydrological responses to transitions in land use/cover and climate impacts within Lake Chilwa Basin in Malawi, using the soil and water assessment tools (SWAT). Results show that deforestation and cropland expansion largely characterized the basin, particularly in the 2000s decade. SWAT model proved highly effective in analyzing impacts of environmental changes, with indicators such as Nash–Sutcliffe efficiency (Ens), Per cent bias (PBIAS) and ratio of root mean square error to measured standard deviation (RSR) presenting satisfactory values of; 0.88, 0.86; − 11.6%, − 19.8% and 0.34, 0.37 after calibration and validation, respectively. Comparison of exceedance probability between periods provided evidence of increasing runoff of up to 11% and subsequent declining baseflows linked to deforestation; irrespective of climate influence which portrayed a decrease–increase–decrease decadal impact on streamflow. The study further shows that forest vegetation tended to escalate evapotranspiration (ET), although the forest role of reducing runoff and enhancing groundwater recharge outweighed the ET effect. Since most watersheds in the basin remain significantly deforested, the threat of increased runoff leading to flooding and declining dry-seasonal river flows is certain

Characterisation of dry spells for agricultural applications in Malawi

Abstract Dry spells are one of the climate change hazards that continue to exert pressure on the agriculture sector, hence affecting food security. Understanding dry spell characteristics of an area helps in coming up with interventions and adaptive measures among other advantages. This study aimed at understanding characteristics of dry spells for Malawi by using climate hazards group infrared precipitation with stations precipitation data from 1981 to 2019. The study focused on the spatial distribution, maximum number of dry days, trend of maximum dry days and time of occurrence of dry spells. Data was analysed using Mann–Kendal trend analysis in R software. The results indicate a high number of occurrences of dry spells in the southern region than the other two regions of Malawi. In addition, the southern region experienced the highest maximum number of dry days. However, there is an upward trend for maximum days of dry spells in central region than all other regions. Local scale topographic influences on dry spell occurrence were also apparent. The study further established that the number of dry spell occurrence in the rainfall season starts to increase towards end of March. In this regard, although rainfall season in the study area is considered to be from November to April, the study recommends that growing season should be considered to be November to March so that crops are not affected by end of season dry spells which are common. Farmers should ensure that they plant crops that will mature with this growing period