Complementary distance Seidel equienergetic graphs

Gopalapillai, Indulal G; Scaria, Deena; Mary, Jinu

doi:10.22061/jdma.2025.12527.1165

Complementary distance Seidel equienergetic graphs

Document Type : Full Length Article

Authors

¹ Department of Mathematics, St. Aloysius College, Edathua, Alappuzha-689573, Kerala, India

² Department of Mathematics, Mar Thoma College, Tiruvalla, Pathanamthitta-689103, India

10.22061/jdma.2025.12527.1165

Abstract

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 ∂₁^S ≥ ∂₂^S ≥ … , ∂_n^S, 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.

Graphical Abstract