In this paper, we first study $fs$-modules, i.e., modules with finitely many small submodules. We show that every $fs$-module with finite hollow dimension is Noetherian. Also, we prove that an $R$-module $M$ with finite Goldie dimension, is an $fs$-module if, and only if, $M = M_1 \oplus M_2$, where $M_1$ is semisimple and $M_2$ is an $fs$-module with $Soc(M_2) \ll M$. Then, we investigate multiplication $fs$-modules over commutative rings and we prove that the lattices of $R$-submodules of $M$ and $S$-submodules of $M$ are coincide, where $S=End_R(M)$. Consequently, $M_R$ and $_SM$ have the same Krull (Noetherian, Goldie and hollow) dimension. Further, we prove that for any self-generator multiplication module $M$, to be an $fs$-module as a right $R$-module and as a left $S$-module are equivalent.

On analyzing the Euclidean graph of fullerene C60, we have obtained the automorphism group of the Euclidean graphs of this molecule. It is proven that this group has order 120 and is isomorphic to Z2 x A5, where Z2 is a cyclic group of order 2 and A5 is the alternating group on five symbols.

Let G be a simple connected graph. In this paper, Szeged dimension and PIv dimension of graph G are introduced. It is proved that if G is a graph of Szeged dimension 1 then line graph of G is 2-connected. Trees of Szeged dimension 1 are characterized. The Szeged dimension and PIv dimension of five composite graphs: sum, corona, composition, disjunction and symmetric difference with strongly regular components are computed. Also explicit formulas of Szeged and PIv indices for these composite graphs are obtained.