Topological indices are of incredible significance in the field of graph theory. Convex polytopes play a significant role both in various branches of mathematics and also in applied areas, most notably in linear programming. We have calculated some topological indices such as atom-bond connectivity index, geometric arithmetic index, K-Banhatti indices, and K-hyper-Banhatti indices and modified K-Banhatti indices from some families of convex polytopes through M-polynomials. The M-polynomials of the graphs provide us with a great help to calculate the topological indices (...) of different structures. (shrink)

This main aim of this paper is to prove that in a direct commutative BCK-algebra an ideal I is nitely generated if and only if I is a principal ideal. This result generalizes the result obtained by E. Y. Deeba in [2]. We also give an answer to the question posed by E. Y. Deeba in [1]: for what class of BCK-algebras is every Noetherian algebra a principal ideal algebra ?