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.

purpose: scorpions in the middle eastern countries are known as the most widely spread poisonous creatures that cause casualties and death to human being and domestic animals. these creatures are distributed and well established in subtropical regions. among sixteen iranian islands in the persian gulf, kish island is the focus of important internal and foreign industrial and commercial activit...

Metrizable spaces are studied in which every closed set is an α-limit for some continuous map and point. It shown that this property enjoyed by space containing sufficiently many arcs (formalized the notion of a with enough arcs), though such need not be arcwise connected. Further it preserved topological sums, products images quotients. However, positive results do hold metrizable obtained tho...

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.