The Spectrum of Weighted Lexicographic Product on Self-complementary Graphs

The lexicographic product, a powerful binary operation in graph theory, offers methods for creating novel by establishing connections between each vertex of one and every another. Beyond its fundamental nature, this is found various applications across computer science disciplines, including network analysis, data mining, optimization. In paper, we give definition the weight function to product G[H] , which enables us capture intricate interplay among vertices constituent graphs facilitate deeper understanding their relationships. We derive an expression spectrum using spectrums xmlns:xlink="http://www.w3.org/1999/xlink">G xmlns:xlink="http://www.w3.org/1999/xlink">H if self-complementary graph. Through systematic analysis careful computations, comprehensive . Remarkably, reveal intriguing characteristic pertaining self-complementarity within weighted Specifically, show that can be two connected graphs. Furthermore, delve into geometric properties specifically examining Ricci curvature regular rigorous have discovered exhibits lower bound on curvature.