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Author: search.filters.author.Senthil Thilak, A.S.Subject: search.filters.subject.Frame graph

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    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.
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    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.