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\...

A graph $G$ is a non-separating planar if there drawing $D$ of on the plane such that (1) no two edges cross each other in and (2) for any cycle $C$ $D$, vertices not are same side $D$.
 Non-separating graphs closed under taking minors subclass superclass outerplanar graphs.
 In this paper, we show only it does contain $K_1 \cup K_4$ or K_{2,3}$ $K_{1,1,3}$ as minor.
 Furthermore...

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...

A metric graph is a pair (G, d), where G and $$d:E(G) \rightarrow \mathbb {R}_{\ge 0}$$ distance function. Let $$p \in [1,\infty ]$$ be fixed. An isometric embedding of the d) in $$\ell _p^k = (\mathbb {R}^k, d_p)$$ map $$\phi :V(G) {R}^k$$ such that $$d_p(\phi (v), \phi (w)) d(vw)$$ for all edges $$vw\in E(G)$$ . The _p$$ -dimension least integer k there exists an _p^k$$ functions d has _p^K$$...

The feasible region $\Omega_{{\rm ind}}(F)$ of a graph $F$ is the collection points $(x,y)$ in unit square such that there exists sequence graphs whose edge densities approach $x$ and induced $F$-densities $y$. A complete description not known for any with at least four vertices clique or an independent set. provides lot combinatorial information about $F$. For example, supremum $y$ over all $(...

Based on the Hugenholtz–Van Hove theorem, six basic quantities of EoS in isospin asymmetric nuclear matter are expressed terms nucleon kinetic energy t(k), symmetric and parts single-nucleon potentials $$U_0(\rho ,k)$$ $$U_{\text {sym},i}(\rho . The include quadratic symmetry $$E_{\text {sym,2}}(\rho )$$ , quartic {sym,4}}(\rho their corresponding density slopes $$L_2(\rho $$L_4(\rho incompress...

Abstract Exchange bias (EB) occurring in ferromagnetic (FM)/antiferromagnetic (AFM) bilayers conventionally can lead to a unidirectional magnetic anisotropy ( K eb ) as well an accompanied unia...

Abstract Claviceps purpurea causing ergot maintains to be a problem in commercial cytoplasmic male sterile (CMS)-based hybrid rye growing. The fungal spores compete with pollen during flowering and incidence is reduced highly pollen-shedding stands. This study was carried out identify maternal differences infection the absence of pollen. Ten male-sterile single crosses were tested by needle spr...

Recently, Dvo\v{r}\'ak, Norin, and Postle introduced flexibility as an extension of list coloring on graphs [JGT 19']. In this new setting, each vertex $v$ in some subset $V(G)$ has a request for certain color $r(v)$ its colors $L(v)$. The goal is to find $L$ satisfying many, but not necessarily all, the requests. main studied question whether there exists universal constant $\epsilon >0$ such ...