Browsing by Author "Weerasinghe, M. H. L."

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Exploring signed domination number for the cartesian product of two path graphs
(Faculty of Science, University of Kelaniya Sri Lanka, 2024) Samaranayaka, K. V. H. C.; Weerasinghe, M. H. L.; Wijesiri, G. S.
Let 𝐺 = (𝑉, 𝐸) be a graph with the vertex set 𝑉(𝐺) and consider a function 𝑓: 𝑉(𝐺) → {-1, +1}. If the closed neighborhood of 𝑣 contains +1′s more than -1′s for every 𝑣 ∈ 𝑉(𝐺). Then 𝑓 is the signed domination function for the graph 𝐺 (1). 𝛾𝑠(𝐺) denotes the minimum weight of a signed domination function of 𝐺. The Cartesian product of two path graphs forms a grid graph. Specially, the Cartesian product of 𝑃𝑚 and 𝑃𝑛 gives 𝑚 × 𝑛 grid graph (𝑚 rows and 𝑛 columns) with 𝑚𝑛 number of vertices. In this study, we review existing methods for determining the signed domination number of the Cartesian product of two path graphs 𝛾𝑠(𝑃𝑚 × 𝑃𝑛). We then include definitions of open and closed neighborhoods of a graph, the signed domination function and the signed domination number. The theorems which are used to determine 𝛾𝑠(𝑃𝑚 × 𝑃𝑛) when 𝑚 = 3,4,5,6 and 7 were also presented. In exploring the 𝛾𝑠(𝑃𝑚 × 𝑃𝑛) where 𝑚 = 8, we draw upon existing literature which has focused on determining signed domination number for 𝛾𝑠(𝑃𝑚 × 𝑃𝑛) ranging from 𝑚 = 3 to 𝑚 = 7. This foundational knowledge guides our approach as we compile graphical illustrations that depict both trivial and general configurations of signed domination in grid graphs. These illustrations help us identify and categorize specific cases, defining sub-cases essential for the proof of the theorem. Through this process, we establish relationships among these graphical representations and develop a localized function, denoted as |𝐵𝑗|, to capture the relationships within each identified case. Building on these insights, we suggest theoretically valid approaches to completing the calculation for the 𝛾𝑠(𝑃𝑚 × 𝑃𝑛) when 𝑚 = 8, evaluating and refining our results based on the findings obtained from these methodical investigations. Our finding leads to a upper bound for the signed domination number of the grid graph 𝑃8 × 𝑃𝑛. The theorem is, for 𝑛 ≥ 1, if 𝑛 ≡ 0(𝑚𝑜𝑑 4) then 𝛾𝑠(𝑃8 × 𝑃𝑛) ≤ 4𝑛. We also propose a conjecture for the 𝑛 ≡ 1(𝑚𝑜𝑑 4), 𝛾𝑠(𝑃8 × 𝑃𝑛) ≤ 4𝑛 + 2.
Facebook Network Analysis Based on Graph Theory
(Faculty of Science, University of Kelaniya Sri Lanka, 2023) Koralegedara, H. C.; Weerasinghe, M. H. L.
In the present world social media has become an essential part of humans' life. Most people use social networks to do their day today life activities. Analyzing real world social networks is also a very important and emerging research area. This research work mainly focused on Facebook social network and analyzed its properties using graph theory concepts. The network is assumed as a graph, that is, a set of vertices (or nodes) representing a person and a set of lines (or edges) representing one or more social relations among them. Graph theory techniques and properties help to analyze and visualize the behavior of networks. To construct our Facebook network, we collected real world data set by doing survey from group of university students. According to our data set we construct a network with 221 nodes and 698 edges to represent our Facebook model. To construct the Facebook model, we used Gephi, which is an open-source software for analyzing and visualizing networks. Real world networks are very complex and massive, and it is not easy to analyze. To analyze our Facebook network model, we basically used content analysis under the following categories such as metric, network structure, temporal, random walks, and visualization. Network metrics identify the most important or central character of the network. Under metric analysis we discussed homophily, density, centrality, and transitivity those are measure principal nodes in a network tends to have links to other nodes, how close the network is to complete, the most influential character of the network and tendency of the nodes to cluster together, respectively. In our model graph density is very low compared with complete. Closeness centrality is very low in the network and it is represented the connections among the people who are in the network is very distant. In the network structure basically discussed how we explore network from its structure, based on two areas such as network features and community detection. The page rank, Hyperlink – Induced Topic Search (HITS) and Stochastic Approach for Link Structure Analysis (SALSA) discussed under random walk. Random Walks is a path across a network created by taking repeated random steps. By temporal we analyze the explicit time dependent properties of the network. Probabilistic ties, time aggregated, media matrix, multi agent and discretization discussed under temporal. Visualization of the network is important, but it is impractical with the very large dataset. This work mainly focusses on analyzing our constructed Facebook model using graph theory properties. The method we used can be applied to find many interesting information in social networks.
Numerical evaluation of wave energy absorption and performance of a selection of wave energy converters in southern sea conditions of Sri Lanka
(Faculty of Science, University of Kelaniya Sri Lanka, 2022) Vishvanath, N. A. V.; Weerasinghe, M. H. L.; Hansameenu, W. P. T.
Ocean wave energy is undoubtedly the next crucial step in Sri Lanka’s energy sector. The abundance of this source of green energy, mainly in the Southern seas of Sri Lanka, has been identified and estimated in a handful of preliminary studies. In the present work, three wave energy converters are numerically modelled with the objective of estimating annual average electrical power and variations in seasonal average electrical power. A 1-body point absorber, 2-body point absorber, and an oscillating surge flap are simulated in sea conditions native to Tangalle, Galle, and Matara generated using measured and re-analysis data. The selection of the devices is mainly based on the depth of the location at which the data is available. The open-source numerical wave energy converter simulating software WEC-Sim is used as the dynamic equation solver, while the open-source Boundary Element Method code NEMOH is used to calculate hydrodynamic parameters. The power take-off is modelled as a linear spring-damper system in all three cases. A damping coefficient optimisation procedure is carried out using samples drawn from each set of data in which a comparative analysis was done to select the damping values that give the maximum power output. Under the optimised damping conditions, mechanical power matrices are generated which are then converted to electrical power matrices using a PTO efficiency conversion factor. Annual and seasonal average power outputs are calculated utilizing both electrical power matrices and joint probability distributions of sea states. The electrical power matrices generated for the 2-body point absorber, and oscillating surge flap are a clear indication that both the devices are naturally tuned to the dominant wave frequencies of tested locations, while the 1-body point absorber is tuned to sea states with lower periods. The highest output power is observed for oscillating surge flap, the second highest for the 2-body point absorber, and the lowest for the 1-body point absorber. The variation of the seasonal average power is significant over the four climatic seasons of Sri Lanka. The highest power observed in South-West monsoon is more than twice the lowest observed in North-East monsoon. The calculated annual average power and seasonal average power outputs are a clear indication of Sri Lanka’s potential for wave energy harvesting, although the greater variation in seasonal average power poses a considerable challenge.