Faculty Publications
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Item Changing and unchanging efficient domination in graphs with respect to edge addition(Cambridge Scientific Publishers boch@lnfm1.sai.msu.ru, 2020) Senthil Thilak, A.S.; Shet, S.V.; Kamath, S.S.A dominating set S of a graph g is an efficient dominating set (EDS) of g if Ng[v]?S=1, for all v e V(g). g is efficiently dominatable or efficient if it has an EDS. Not all graphs are efficient. The class of efficient graphs is denoted by E. If g e E, then any EDS of g has its cardinality equal to the domination number of g, denoted by g(g). An edg+e e e E(g) is critical or g-critical if y(g+e) ? y(g). The study of critical concepts exists for domination and its variants. We extend this study to graphs which are efficient. This paper deals with the study of the properties of critical edg+es of graphs in E. Depending on whether the addition of an edg+e increases or decreases or leaves unaltered g(g), the edg+e set of g is classified respectively into three sets: EA+, EA-, EA0. To study the changing and unchanging property of efficient domination, we define the classes UEAE = UEA? g+e, CEAE = CEA?g+e, where g+e = {g: g ? E and g+e ? E, for all e ? E(g)g, UEA = (g: g(g) = g(g+e), for all e ? E(g)g and CEA = (g: g(g) ? g(g+e), for all e ? E(g)g. We characterize the critical edg+es, edg+e critical sets, the two classes of graphs defined above and identify their relationship with critical vertices of those graphs in E. We also identify the relationship between all classes of graphs resulting from vertex criticality (vertex removal) and edg+e criticality (edg+e removal and edg+e addition) and represent through Venn diagram. This study plays a significant role in the analysis and design of fault tolerant networks. © 2020 by the authors.Item ON THE CONSTRUCTION AND PROPERTIES OF FRAMES USING INCIDENCE MATRIX OF GRAPHS AND THEIR SPECTRA(Jangjeon Research Institute for Mathematical Sciences and Physics, 2024) Senthil Thilak, A.S.; Ayyanar, K.; Johnson, P.S.Frames are considered to be redundant counterparts of bases for vector spaces. This redundant structure favours frames to be rich in both theory and applications. In recent studies on frames, graph theory is one of the significant tools to analyze the properties of different types of frames. In graph theory, we associate a graph with different types of matrices, of which signless Laplacian matrix contributes significantly in exploring the properties of a graph. In this paper, given a graph G, we propose a method to construct a frame from its incidence matrix such that its frame graph is the line graph of a derived graph of G. We analyze various properties of the frame constructed as above, its dual, etc. Further, we investigate the existence of frames with constrained frame bounds, using the properties of the associated graph and its signless Laplacian spectrum. © 2024 Jangjeon Research Institute for Mathematical Sciences and Physics. All rights reserved.Item A unified vehicle trajectory prediction model using multi-level context-aware graph attention mechanism(Springer, 2024) Sundari, K.; Senthil Thilak, A.S.Predicting the mobility patterns of vehicles together with their interactions among surrounding traffic objects is a critical task in autonomous driving systems. Existing graph neural network-based trajectory prediction models primarily capture the structural connectivity of network nodes (road objects) and assume equal priority to all neighbors of a node. However, in real-time traffic networks, the behavior of each vehicle is significantly influenced by its neighboring road objects and this influence is not uniform. This necessitates a neighbor interaction-aware trajectory prediction model that assumes non-uniform priority among neighboring nodes. In this article, we have designed a novel unified trajectory prediction model which is suitable for both highway and urban traffic conditions. The proposed approach seamlessly integrates multi-level context modeling using graph attention mechanisms, capturing and leveraging interactions and dependencies among objects at varied levels of proximity within a graph. Additionally, it employs an encoder–decoder long short-term memory architecture for long-term trajectory prediction, ensuring adaptability to different driving scenarios. The advanced graph attention mechanisms play a crucial role in modeling spatial dependencies between vehicles, allowing the proposed model to dynamically adapt to evolving interactions over time. The experimentations done on real-world trajectory datasets, namely, Next Generation Simulation US-101 highway dataset and diverse urban datasets such as ApolloScape and Argoverse demonstrate remarkable performance of MC-GATP in long-term trajectory prediction. The model showcases superior prediction accuracy, scalability, and computational efficiency for both highway and urban environments. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024.Item Frame Scaling by Graphs(Indian National Science Academy, 2025) Ayyanar, K.; Johnson, P.; Senthil Thilak, A.S.In this paper, we investigate the scalability of a given frame in Rn by using graphs. For each frame ? in Rn, we associate a simple undirected graph G(?) and use it to verify the scalability of ?. We provide some necessary conditions to test the scalability of a given frame. Finally, we study the scalability of some special classes of frames by using graphs. © The Indian National Science Academy 2025.Item A deep learning approach to predicting vehicle trajectories in complex road networks(Springer Science and Business Media Deutschland GmbH, 2025) Sundari, K.; Senthil Thilak, A.S.Accurate prediction of vehicle trajectories is essential for safe and efficient navigation in urban environments, particularly with the increasing prevalence of autonomous vehicles and intelligent transportation systems. This paper introduces a deep learning-based approach for predicting vehicle trajectories on urban roads in real time. The method combines techniques from graph neural networks (GNNs) and long short-term memory (LSTM)-based models to capture intricate spatial and temporal dependencies among vehicles. Vehicles are represented as nodes in the proposed graph model, and graph attention mechanism is used to model the interactions between them. Additionally, LSTM modules encode motion patterns and temporal correlations, facilitating spatial and temporal information fusion to improve prediction accuracy. The effectiveness of the approach is demonstrated through extensive experimentation and evaluation in generating vehicle trajectories, surpassing baseline methods. The proposed method holds promise for real-time vehicle trajectory prediction, with the potential for applications in autonomous driving, traffic management, and intelligent transportation systems. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024.