The order graph of a group $G$, denoted by $Gamma^*(G)$, is a graph whose vertices are subgroups of $G$ and two distinct vertices $H$ and $K$ are adjacent if and only if $|H|big{|}|K|$ or $|K|big{|}|H|$. In this paper, we study the connectivity and diameter of this  graph. Also we give a relation between the order graph and prime  graph of a group.

let $k$ be a positive integer. a subset $s$ of $v(g)$ in a graph $g$ is a $k$-tuple total dominating set of $g$ if every vertex of $g$ has at least $k$ neighbors in $s$. the $k$-tuple total domination number $gamma _{times k,t}(g)$ of $g$ is the minimum cardinality of a $k$-tuple total dominating set of $g$. if$v(g)=v^{0}={v_{1}^{0},v_{2}^{0},ldots ,v_{n}^{0}}$ and $e(g)=e_{0}$, then for any in...

Genes in human chromosomes that normally require induction by alpha-interferon are activated after calcium phosphate (CaPO4) transfection, but not after DEAE-dextran transfection. The c-fos gene and genes stimulated by gamma-interferon also are affected by CaPO4-DNA precipitates, but the calcium ionophore A23187 stimulates only c-fos among this group. These results suggest caution not only in c...

Inspired by the recent observation of a new structure, $X(4014)$, in process $\gamma\gamma\to \gamma\psi(2S)$, we evaluate possibility assigning $X(4014)$ as $D^\ast \bar{D}^\ast$ molecular state with $I(J^{PC})=0(0^{++})$ investigating hidden charm decays $X(4014)$. The partial widths $J/\psi\omega$, $ \eta_{c}\eta$ and $\eta_{c}\eta^{\prime}$ channels are evaluated to be about $(0.41\sim 5.00...

The recent BESIII data on $J/\psi\to\gamma(K_SK_S\pi^0)$, which is significantly more precise than earlier $\eta(1405/1475)$-related data, enables quantitative discussions $\eta(1405/1475)$ at the previously unreachable level. We conduct a three-body unitary coupled-channel analysis of experimental Monte-Carlo outputs for radiative $J/\psi$ decays via $\eta(1405/1475)$: $K_SK_S\pi^0$ Dalitz plo...

The current article stems from our study on the asymptotic behavior of holomorphic isometric embeddings Poincaré disk into bounded symmetric domains. As a first result we prove that any curve exiting boundary domain $\Omega$ must necessarily be asymptotically totally geodesic. Assuming otherwise derive by method rescaling hypothetical embedding with $\operatorname{Aut}(\Omega^\prime)$-equivalen...