Several new classes of the algebraic problems are investigated, such as permutation d/d-edge/d-transitive-algebras, permutation d/d#-ideals and permutation d-subalgebras are discussed and looked into. We show that the product for any member in permutation d-algebra from the right with constant is equal the same member. Also, any permutation d-algebra is a permutation d-transitive algebra if and only if its extended edge permutation d-algebra is permutation d-transitive algebra. Additionally, permutation d*-algebra, permutation d-morphism, equivalence relation, congruence class and quotient permutation d-algebras were defined with specific results relating to these new notions are examined.
In this article, we compute the diameter and Wiener index of circulant graphs. We derive a formula for the Wiener index of these graphs, which is given by two forms, depending on the integer l. Furthermore, we explore the diameter of these circulant graphs and prove that diameter is equal 2. Additionally, we establish that the circulant graph exhibits Eulerian properties when the integer l is an odd number. Our finding contribute to the understanding of the structural characteristics and metrics of circulant graphs, providing valuable insights for graph theory and related fields.
In this paper, the notion of an entirely novel type of BP-algebras was introduced. Moreover, their fundamental characteristics were examined. Also, we thought about and talked about and talked about some novel ideas in permutation BP-algebras, such as {1}-commutative permutation BP-algebras, and some relationships with permutation BH- algebras and permutation B-algebras.
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