Given a graph G and positive integer k, define the Gallai-Ramsey number to be minimum of vertices n such that any k-edge coloring $$K_n$$ contains either rainbow (all different colored) triangle or monochromatic copy G. Much like Ramsey numbers, numbers have gained reputation as being very difficult compute in general. As yet, still only precious few sharp results are known. In this paper, we o...

In [16] Nowakowski and Rall listed a series of conjectures involving several different graph products. particular, they conjectured that $$i(G\times H) \ge i(G)i(H)$$ where i(G) is the independent domination number G $$G\times H$$ direct product graphs H. We show this conjecture false, and, in fact, construct pairs for which $$\min \{i(G), i(H)\} - i(G\times H)$$ arbitrarily large. also give ex...

In this paper, we introduce the concept of semihyperring $(R,+,cdot)$ together with a suitable partial order $le$. Moreover, we introduce and study hyperideals in ordered semihyperrings. Simple ordered semihyperrings are defined and its characterizations are obtained. Finally, we study some properties of quasi-simple and $B$-simple ordered semihyperrings.

In this paper, the author studied skeletal congruences θ^* of a distributive nearlattice S, where * represents pseudocomplement. Then described θ(I)^*, θ(I) is smallest congruence S containing n-ideal I as class and showed that I^+ n-kernel θ(I)^*. established following fundamental results: When n an upper element has shown n-kernels are precisely those n-ideals which intersection relative anni...

We present an INTEGRAL data analysis of the X-ray transient SAX J2103.5+4545 during two outbursts detected in December 2002. The INTEGRAL coordinates and error circle agree with the position of the recently proposed optical counterpart. A power-law plus cutoff model provided a good fit to the 4–150 keV spectrum yielding a photon index of 1.0±0.1, a cutoff energy E cut = 7.6 ± 2.0 keV and a fold...

By a Riemann function we mean $f:\mathbb{Z}^n\to\mathbb{Z}$ such that $f(\mathbf{d})$ is equals $0$ for $d_1+\cdots+d_n$ sufficiently small, and $d_1+\cdots+d_n+C$ constant, $C$, large. adding $1$ to the Baker-Norine rank of graph, one gets an equivalent function, similarly related functions.
 To each associate $W: \mathbb{Z}^n\to \mathbb{Z}$ via Möbius inversion call weight function. We g...

In this paper we introduce generalized Darboux frame of a spacelike curve $\alpha$ lying on lightlike surface in Minkowski space $\mathbb{E}_{1}^{3}$. We prove that has two such frames and obtain frame's equations. find the relations between curvature functions $k_g$, $k_n$, $\tau_g$ with respect to its $\tilde{k}_{g}$, $\tilde{k}_{n}$, $\tilde{\tau}_{g}$ frames. show exist along straight line ...