‎Let $R$ be a commutative ring with non-zero identity. ‎We describe all $C_3$‎- ‎and $C_4$-free intersection graph of non-trivial ideals of $R$ as well as $C_n$-free intersection graph when $R$ is a reduced ring. ‎Also, ‎we shall describe all complete, ‎regular and $n$-claw-free intersection graphs. ‎Finally, ‎we shall prove that almost all Artin rings $R$ have Hamiltonian intersection graphs. ...

Let $\mathbf L_k$ be the holomorphic line bundle of degree $k \in \mathbb Z$ on projective line. Here, tuples $(k_1 k_2 k_3 k_4)$ for which there does not exists homogeneous non-split supermanifolds $CP^{1|4}_{k_1 k_4}$ associated with vector L_{−k_1} \oplus \mathbf L _{−k_2} L_{−k_3} L_{−k_4}$ are classified. \\For many types remaining tuples, listed cocycles that determine supermanifolds. \\P...

Let $$G=(V,E)$$ be a finite graph (here V and E denote the set of vertices edges G respectively) $$M_G$$ centered Hardy–Littlewood maximal operator defined there. We find optimal value $$\mathbf{{C}}_{G,p}$$ such that inequality $$\begin{aligned} \mathrm{Var\,}_{p}M_{G}f\le \mathbf{C}_{G,p}\mathrm{Var\,}_{p}f \end{aligned}$$ holds for every $$f:V\rightarrow {\mathbb {R}},$$ where $$\mathrm{Var\...

in this paper, it is proved that all simple $k_4$-groups of type $l_2(q)$ can be characterized by their maximum element orders together with their orders. furthermore, the automorphism groups of simple $k_4$-groups of type $l_2(q)$ are also considered.

Given a finite graph G, the maximum length of sequence $$(v_1,\ldots ,v_k)$$ vertices in G such that each $$v_i$$ dominates vertex is not dominated by any $$\{v_1,\ldots ,v_{i-1}\}$$ called Grundy domination number, $$\gamma _\mathrm{gr}(G)$$ , G. A small modification definition yields Z-Grundy which dual invariant well-known zero forcing number. In this paper, we prove _\mathrm{gr}(G) \ge \fra...