Faculty of Sciencehttp://hdl.handle.net/10646/13802017-09-19T22:30:23Z2017-09-19T22:30:23ZAverage distance and edge-connectivity IDankelmann, PeterMukwembi, SimonSwart, Henda Chttp://hdl.handle.net/10646/33812017-09-06T07:43:37Z2015-01-15T00:00:00ZAverage distance and edge-connectivity I
Dankelmann, Peter; Mukwembi, Simon; Swart, Henda C
The average distance $\mu(G)$ of a connected graph G of order n is the average of the distances between all pairs of vertices of G. We prove that if G is a $\lambda$-edge-connected graph of order n, then the bounds $\mu(G) \le 2n/15+9$ if $\lambda=5,6$, $\mu(G) \le n/9+10$ if $\lambda=7$, and $\mu(G) \le n/(\lambda+1)+5$ if $\lambda \ge 8$ hold. Our bounds are shown to be best possible, and our results solve a problem of Plesník
The results in this paper are part of the second author’s PhD thesis.
2015-01-15T00:00:00ZMinimum degree, leaf number and traceabilityMukwembi, Simonhttp://hdl.handle.net/10646/33802017-09-06T07:35:23Z2013-03-26T00:00:00ZMinimum degree, leaf number and traceability
Mukwembi, Simon
Let G be a finite connected graph with minimum degree δ. The leaf number L (G) of G is defined as the maximum number of leaf vertices contained in a spanning tree of G. We prove that if δ >12(L (G) + 1), then G is 2-connected. Further, we deduce, for graphs of girth greater than 4, that if δ>12(L (G) + 1), then G contains a spanning path. This provides a partial solution to a conjecture of the computer program Graffiti.pc [DeLaVi ̃na and Waller, Spanning trees with many leaves and average distance, Electron. J. Combin. 15 (2008), 1–16]. For G claw-free, we show that if δ >12(L (G) + 1), then G is Hamiltonian. This again confirms, and even improves, the conjecture of Graffiti.pc for this class of graphs.
This paper was written during the author’s Sabbatical visit at the University of Zimbabwe, Harare.
2013-03-26T00:00:00ZSpatiotemporal patterns of clinical bovine dermatophilosis in Zimbabwe 1995-2014Ndhlovu, Daud N.Chikerema, Sylvester M.Masocha, MhosisiNyagura, MudavanhuPfukenyi, Davies M.Ndhlovu, Felistashttp://hdl.handle.net/10646/33792017-09-06T07:17:58Z2017-06-27T00:00:00ZSpatiotemporal patterns of clinical bovine dermatophilosis in Zimbabwe 1995-2014
Ndhlovu, Daud N.; Chikerema, Sylvester M.; Masocha, Mhosisi; Nyagura, Mudavanhu; Pfukenyi, Davies M.; Ndhlovu, Felistas
A retrospective study of clinical bovine dermatophilosis outbreaks and cases for the period 1995-2014 was conducted, using data obtained from the Division of Veterinary Services (DVS). A total of 3856 outbreaks and 26 659 cases of dermatophilosis were reported countrywide during this period. The post rainy season accounted for 37.9% of the outbreaks followed by the rainy season (26.7%), cold dry season (22.1%) and the hot dry season (13.2%). A retrospective space-time scan statistic in SaTScan™ was used to detect clusters. From this study, it was evident that dermatophilosis was spreading from the north-west of Zimbabwe through the central to the north-east during the period 2010-2014. Five clusters were identified mainly in the central and north-western regions of Zimbabwe. The primary cluster was centred at Ungwe, Gokwe district in Midlands; the second, third, fourth and fifth likely clusters were centred at Bonga (Mashonaland Central), ARDA (Mashonaland West), Nsenga (Matabeleland North) and Zanda in Gokwe, respectively. The findings of this study suggest the continued spread of dermatophilosis across the country; as such the Department of Livestock and Veterinary Services are advised to develop measures aimed at managing this spread such as dipping, quarantine, movement control and raising farmer awareness.
2017-06-27T00:00:00ZExtraction and characterisation of phytochemicals from white seringa (kirkia acuminata) bark extractsChinheya Mhlanga, Rosahttp://hdl.handle.net/10646/31032017-04-13T09:03:10Z2016-10-01T00:00:00ZExtraction and characterisation of phytochemicals from white seringa (kirkia acuminata) bark extracts
Chinheya Mhlanga, Rosa
The intention of this study was to extract and characterise phytochemicals with analgesic effect from Kirkia Acuminata bark extracts. Soxhlet extraction and Steam distillation were used for the extraction of compounds. Methanol,dichloromethane and hexane were used as solvents. Classes of phytochemicals were identified by qualitative tests and Thin Layer Chromatography using UV light.The qualitative tests of the phytochemical screening indicated the presence of alkaloids, anthraquinones, glycosides, flavonoids, phenols, tannins to name a few. Alkaloids, flavonoids, phenols and tannins were also observed on Thin Layer Chromatography. Menthol, catechol, 1,2 benzenediol 4 methyl, nitro phenyl salicylate, phenol dimethoxy,tau-cadinol,Isopropenyl,8 dimethyl, menthone and levomenthone were identified using Gas Chromatography-Mass Spectrometer.. The hexane fraction which is highly a non-polar solvent showed that very few phytochemicals were taken up in it.The polar solvents showed compatibility with the various chemical classes. The presence of these compounds gives Kirkia acuminataits characteristic property of being an analgesic. It thus finds application in the field of medicine.
2016-10-01T00:00:00Z