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In the field of Theoretical Computer Science and Molecular Biology, Combinatorics on words has contributed a lot and has a wide range of applications in cancer cell detection, pattern matching and fractal geometry. Motivated by the concept of word graphs, in this paper, construction of a Generalized k−Modulo Graph and Generalized Complement of k−Modulo Graph are initiated. Subgraph properties are analysed and also adjacency matrix is discussed. Finally, Spectrum of graphs are calculated and a comparative relation is shown. [ABSTRACT FROM AUTHOR]

In this research article, k — Modulo Infinite Array and Complement of k — Modulo Infinite Array are introduced. The algebraic and Circulant properties for k — Modulo Infinite Array and Complement of k — Modulo Infinite Array are deliberated. The Norm and Spectrum of k — Modulo Infinite Array are derived and generalized for any dimension. The Generalized inverse is existed for k — Modulo Infinite Array and Complement of k — Modulo Infinite Array and also the Special inverses are elaborated. The subarrays of k — Modulo Infinite Array and Complement of k — Modulo Infinite Array have inherited the existence of Special inverses such as Quasi Commuting inverse, Drazin inverse and Group inverse, which are explored with suitable numerical illustrations. [ABSTRACT FROM AUTHOR]