As an extension of the class of (pre)-Schreier domains introduced by P. M. Cohn and M. Zafrullah, we introduce and study a class of integral domains D characterized by the property that whenever a b 1 b 2 ∈ D − 0 and a b 1 b 2 , there exist an integer k ≥ 1 and a 1 a 2 ∈ D − 0 such that a k = a 1 a 2 and a i b k i , i = 1 2. We call them almost-Schreier domains. We show that an almost-Schreier domain has torsion t-class group, that a local (Noetherian) one-dimensional domain is almost-Schreier and that the polynomial ring with coefficients in an integrally closed almost-Schreier domain is almost-Schreier.
The application of graph theory in chemical and molecular structure research far exceeds people's expectations, and it has recently grown exponentially. In the molecular graph, atoms are represented by vertices and bonded by edges. In this report, we study the Zagreb-polynomials of line graph of HAC 5 C 6 C 7 [p, q] and compute some degree-based topological indices from it.
The application of graph theory in chemical and molecular structure research far exceeds people's expectations, and it has recently grown exponentially. In the molecular graph, atoms are represented by vertices and bonded by edges. In this report, we study the M-polynomial of line graph of HAC 5 C 6 C 7 [p, q] and recover many degree-based topological indices from it.
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