Shahid Rajaee Teacher Training University Journal of Discrete Mathematics and Its Applications 2981-0809 11 2 2026 06 01 Complementary distance Seidel equienergetic graphs 99 106 12569 10.22061/jdma.2025.12527.1165 EN Indulal G Gopalapillai Department of Mathematics, St. Aloysius College, Edathua, Alappuzha-689573, Kerala, India Deena Scaria Department of Mathematics, St. Aloysius College, Edathua, Alappuzha-689573, Kerala, India Jinu Mary Department of Mathematics, Mar Thoma College, Tiruvalla, Pathanamthitta-689103, India Journal Article 2025 09 18 The distance matrix, its eigenvalues, and the corresponding distance energy of a connected graph have been extensively studied in the literature. However, research on the Distance Seidel matrix associated with a connected graph remains in its developmental stages. The Distance Seidel matrix of a graph yields the Distance Seidel eigenvalues ∂1S ≥ ∂2S ≥ … , ∂nS, which together constitute the Distance Seidel spectrum of G. In [1], the authors introduced the complementary distance matrix and studied its properties. Motivated by these we introduce the complementary distance seidel matrix of a connected graph and obtain some results for some classes of graphs. In this paper, we investigate the Complementary Distance Seidel Spectrum of complement of line graphs of regular graphs.

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