Browsing by Author "Perera, K. K. K. R."

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Energies of graphs by means of splitting and shadow graph operations
(Faculty of Science, University of Kelaniya Sri Lanka, 2023) Samarasinghe, S. V. S. K.; Perera, K. K. K. R.
Chemical applications of graph theory were presented by Hückel in his molecular orbital theory. In mathematical chemistry, the skeleton of non-saturated hydrocarbon is represented by a graph which is called the molecular graph. The energy levels of electrons are eigenvalues of the graph, and the strength of particles is closely identified with the spectrum of its graph. The sum of the absolute values of eigenvalues of the adjacency matrix of a simple, finite, and undirected graph G was defined as the energy of G. After the success of this theory, numerous various graph energies were introduced, using different matrices other than adjacency matrix, such as Laplacian energy and Randić energy from Laplacian and Randić matrices respectively. Applications of graph energy appeared in quantum chemistry to determine different characteristics of molecules. Graph energy is related to π-electron energy of a molecule, the generalized ABC energy is related to the polarization of bonds in a molecule, and the harmonic energy is a useful tool in predicting the boiling point, heats of vaporization, surface tensions and critical temperature of alkanes with high correlation coefficient values. There are many graph operations such as graph union, graph intersection, graph join, that can be used to obtain different graphs from a given graph. In this study, splitting and shadow graph operations will be discussed. These two graph operations enable us to acquire bigger graphs from a given graph. The objective of this research is to find generalized ABC energy, sum-connectivity energy and harmonic energy of much bigger graphs acquired from the given graph using the above graph operations. This allows us to obtain ABC energy, sumconnectivity energy and harmonic energy of bigger graphs using those energies of rather small graphs. Direct relationship between the original graph various energy and the relevant energy of the larger graph can be observed from the results. In this research, ABC energy of the splitting graph and shadow graph of any k-regular graph, and the sum-connectivity energy and harmonic energy of the shadow graph of any graph were obtained. These results were novel and verified through the simulations.
Graph theoretical analysis of tuberculosis transmission in Western Province, Sri Lanka with integrated forecasting and TOPSIS
(Faculty of Science, University of Kelaniya Sri Lanka, 2024) Perera, P. N. M.; Perera, K. K. K. R.
Tuberculosis (TB), caused by Mycobacterium tuberculosis, remains a persistent global health challenge, particularly prevalent in low- and middle-income countries due to socioeconomic disparities and limited healthcare access. This study focuses on the Western Province of Sri Lanka, characterized by dense population centres, extensive trade, tourism, and significant urban-rural mobility, all contributing factors to the rapid spread of TB. The research aims to refine TB control strategies through several key objectives. First, the study forecasts TB cases for 2022 across genders, age groups, and types of TB using data up to 2021. Despite lacking comprehensive data beyond 2022, the methodological framework and insights offer valuable guidance for future research and public health strategies. This limitation underscores the need for continued data collection and analysis to refine predictive models and enhance TB control measures. Second, the research involves constructing a comprehensive patient data table integrating demographic details, TB types, and contact information of TB patients in the Western Province. Third, the study uses patient contact data to create a TB contact network model representing disease transmission dynamics. Principles of graph theory, particularly those within social network analysis, are then applied to analyze the network, focusing on metrics such as closeness and betweenness centrality to identify influential nodes and structural characteristics like modularity and average clustering coefficient to understand community formations. Fourth, the study implements the TOPSIS method to rank nodes within the TB contact network based on their potential to spread TB, aiding in identifying critical nodes for targeted intervention strategies. Data collection included compiling TB annual reports from 2012 to 2021 from the National Programme for Tuberculosis Control and Chest Diseases (NPTCCD) website, and statistical forecasts for 2022 were generated using ARIMA models in R, projecting TB cases by gender, age groups, and TB type. Descriptive statistics highlighted demographic trends, with male patients and the 55-64 age group projected to have higher TB incidence rates, primarily pulmonary TB cases. Network analysis revealed a low average clustering coefficient (0.002) and a high modularity value (0.856), indicating sparse local connections and strong community structures within the TB contact network. Comparative analysis pre- and post-TOPSIS implementation demonstrated an enhanced ability to pinpoint influential spreaders, enhancing the precision of targeted intervention strategies. This study underscores the importance of tailored medical and community-based interventions in the Western Province to effectively mitigate TB transmission, emphasizing optimizing TB control measures and improving treatment outcomes.
The Holt-Winters’ method for forecasting water discharge in Attanagalu Oya
(Faculty of Science, University of Kelaniya, Sri Lanka., 2021) Anuruddhika, M. L. P.; Premarathna, L. P. N. D; Perera, K. K. K. R.; Hansameenu, W. P. T.; Weerasinghe, V. P. A.
Forecasting river water discharge is significant in developing flood and agriculture management plans. Annual flood events damage properties, agricultural field, and infrastructures, etc. can be observed in Attanagalu Oya catchment area in Sri Lanka. Therefore, the aim of this study is to forecast water discharge rates (m3/s) at the Dunamale gauging station of Attanagalu Oya using Holt-Winter's method. Holt-Winter's method was chosen because of its’ ability to model trend and seasonal fluctuations, less data requirements and simplicity. Time series models were fitted using the Holt-Winter's method to daily water discharge rates for the period of 2015 –2019 and water discharge was forecasted for the year 2020. The accuracy of the fitted time series models was tested using root mean squares error (RMSE) and mean absolute error (MAE) values. Results showed that the additive Holt-Winters’ method is more appropriate for future forecasting which gave the minimum RMSE and MAE values. Forecasted results will be useful to identify future flood events in advanced to take necessary actions to mitigate damages.
Properties of cellular automata on a group
(Research Symposium on Pure and Applied Sciences, 2018 Faculty of Science, University of Kelaniya, Sri Lanka, 2018) Liyanage, T. C.; Perera, K. K. K. R.
A cellular automaton (pl. Cellular Automata(CA)) is a discrete model studied in the fields of Computer science, Mathematics and Theoretical Biology with different purposes such as simulation of natural phenomena and modeling process. A cellular automaton consists of a regular grid of cells. Each cell is represented by on or off state. The dimension of grid can be finite or infinite. The relationship between cellular automata and group theory was studied by T. Ceccherini-Silberstein in 2010. Thereafter, in 2014, S. Inokuchi et al has introduced composition for cellular automata on groups. This study is based on the notion of a cellular automaton and the relation between the cellular automata and groups. We fix a group G and an arbitrary set which is called the alphabet. Then a configuration is defined as a map from the group into the alphabet. The left multiplication in G induces a natural action of G on the set of configurations, which is called the G-shift and all cellular automata will be required to commute with the shift. The memory set of minimal cardinality of cellular automaton is called its minimal memory set. In this research, we prove some properties of cellular automata defined on a group G such as, every cellular automaton is G-equivariant; intersection of two memory sets of a cellular automaton is also a memory set; every bijective cellular automaton is invertible; Cartesian product of two cellular automata is also a cellular automaton. We also find the minimal memory set for some cellular automaton and the number of cellular automata for a finite group.
Topological indices of some anti-cancer molecular graphs and dendrimer structures
(Faculty of Science, University of Kelaniya, Sri Lanka, 2021) Sebastian, S. L. D. J.; Perera, K. K. K. R.
Cancer disease are leading cause of death in the world as well as in Sri Lanka. Anticancer drugs and delivery dendrimers are one of the important medicine in curing cancers. Various experiments were performed to avoid the occurrence of the rapid growth of cancer cells. Because of that study of anti-cancer drugs and dendrimers are particularly important. Topological indices are molecular descriptors, which are numerical values associated with the physical properties of the chemical structure of a molecule. Finding the physical properties of a molecule in a laboratory is an expensive exercise as it requires many compounds, drugs and time. Therefore, by calculating topological indices, it is possible to get the necessary knowledge about molecules. The objective of this study is to compute the degree-based topological indices of some dendrimer structures that were not calculated earlier and predict the physical properties of selected anticancer drugs using linear regression models. In this work, various topological indices were defined on some anticancer drugs and dendrimer structures, which enable the researchers to know the physical, physicochemical, and chemical properties associated with them. Here the molecular structures were represented as hydrogen depleted molecular graphs considering the adjacency relationships among atoms as vertices corresponding to the atoms of the molecular graph and edges corresponding to chemical bonds. Zagreb and Randić indices are the commonly used indices around new drug design and improvement in this category. Therefore, in this study, degree-based topological indices such that Hyper Zagreb Index - HZ(G), Reduced Second Zagreb index - RM2(G), Augmented Zagreb Index - AZI(G), Forgotten Index - F(G), Inverse Sum Index - ISI(G) were calculated for Poly amidoamine (PAMAM), Polypropylene imine (PPI), Triazine drug delivery dendrimers. Considering the degree of the end vertices, topological indices were calculated for the dendrimer graph. The edge set of the whole graph was partitioned into several sets around on their degrees at the end vertices beginning from the dendrimer core unit. Finally, derived general formulas to find topological indices in the nth generation of a dendrimer. For anti- cancer drugs, fifteen drugs approved for Brain tumors, Testicular cancer, and Acute Lymphoblastic Leukemia were selected using the degree-based calculations, physical properties such as Boiling point, Melting point, Flashpoint, Molar Polarizability, Molar Volume, and Molar Refractivity were predicted. The most studied topological indices are vertex degree-based topological indices. For anti-cancer molecular graphs, selected Zagreb indices, Randic indices, Forgotten Index, Inverse Sum Index, Shigenhalli, and Kanabur Indices were calculated. Calculation of topological indices according to the edge partition is carried out and a MATLAB code was developed for the purpose. Finally, the linear regression model between the topological index and selected physical property was fitted using Minitab software. The significance of the study was predicted using the Pearson correlation coefficient. All calculated values were greater than 0.5 and most of them were greater than 0.75. Therefore values were highly positively correlated.