In this paper we consider two pointsets in $ \mathrm{PG}(2,q^n) arising from a linear set L of rank n contained line $: the first one is blocking Rédei type, second extends construction translation KM-arcs. We point out that their intersections pattern with lines related to weight distribution considered $. then Hamming metric codes associated both these constructions, for which can completely ...

Three-dimensional Weyl semimetals have pairs of topologically protected nodes, whose projections onto the surface Brillouin zone are end points zero energy states called Fermi arcs. At endpoints arcs, extend into and hybridized with bulk. Here, we consider a two-dimensional junction two identical surfaces twisted respect to each other tunnel-coupled. Confining ourselves commensurate angles (suc...

We show that the nerve complex of n arcs in the circle is homotopy equivalent to either a point, an odd-dimensional sphere, or a wedge sum of spheres of the same even dimension. Moreover this homotopy type can be computed in time O(n log n). For the particular case of the nerve complex of evenly-spaced arcs of the same length, we determine the dihedral group action on homology, and we relate th...

The 3-arc graph of a digraph D is defined to have vertices the arcs of D such that two arcs uv, xy are adjacent if and only if uv and xy are distinct arcs of D with v 6= x, y 6= u and u, x adjacent. We prove Hadwiger’s conjecture for 3-arc graphs.

Let $D$ be a finite and simple digraph with vertex set $V(D)$. A weak signed Roman dominating function (WSRDF) on is $f:V(D)\rightarrow\{-1,1,2\}$ satisfying the condition that $\sum_{x\in N^-[v]}f(x)\ge 1$ for each $v\in V(D)$, where $N^-[v]$ consists of $v$ allvertices from which arcs go into $v$. The weight WSRDF $f$ $\sum_{v\in V(D)}f(v)$. domination number $\gamma_{wsR}(D)$ minimum $D$. In...

In this paper, studied the types of (k, r)-arcs were constructed by action groups on three-dimensional projective space over Galois field order eight. Also, determined if they form complete arcs or not.

In the traffic equilibrium problem, we introduce capacity constraints of arcs, extend Beckmann’s formula to include these constraints, and give an algorithm for traffic equilibrium flows with capacity constraints on arcs. Using an example, we illustrate the application of the algorithm and show that Beckmann’s formula is a sufficient condition only, not a necessary condition, for traffic equili...

In this paper a 2-arc of size 21 in the projective Hjelmslev plane PHG(2,Z25) and a 2-arc of size 22 in PHG(2,F5[X]/(X)) are given. Both arcs are bigger than the 2-arcs previously known in the respective plane. Furthermore, we will give some information on the geometrical structure of the arcs.