Let G be a (p, q) graph. Let k be an integer with 2 ≤ k ≤ p and f from V (G) to the set {1, 2, . . . , k} be a map. For each edge uv, assign the label |f(u) − f(v)|. The function f is called a k-difference cordial labeling of G if |νf (i) − vf (j)| ≤ 1 and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labelled with x (x ∈ {1, 2 . . . , k}), ef (1) and ef (0) respectively den...

Let T be a finite subset of the complex unit circle S, and define f : S 7→ S by f(z) = z. Let CH(T ) denote the convex hull of T. If card(T ) = N ≥ 3, then CH(T ) defines a polygon with N sides. The N -gon CH(T ) is called a wandering N -gon if for every two non-negative integers i 6= j, CH(f (T )) and CH(f (T )) are disjoint N -gons. A non-degenerate chord of S is said to be critical if its tw...

There are several known results asserting that undirected graphs can be partitioned in a way that satisfies various imposed constrains on the degrees. The corresponding results for directed graphs, where degrees are replaced by outdegrees, often fail, and when they do hold, they are usually much harder, and lead to fascinating open problems. In this note we list three problems of this type, and...

In this paper, we introduce a new function called tri-ĝ continuous in tri-topological spaces. A map f : X → Y is if f-1(V) closed for each tri-closed set V Y. Also define, quasi tri-ĝ. perfectly tri-ĝ, contra totally and strongly maps are introduced some of their properties studied.

It is shown how many techniques of categorical domain theory can be expressed in the general context of topical categories (where \topical" means internal in the category Top of Grothendieck toposes with geometric morphisms). The underlying topos machinery is hidden by using a geometric form of constructive mathematics, which enables toposes as \generalized topological spaces" to be treated in ...

We study exponentiability of homomorphisms in varieties of universal algebras close to classical ones. After describing an “almost folklore” general result, we present a purely algebraic proof of “étale implies exponentiable”, alternative to the topologically motivated proof given in one of our previous papers, in a different context. We prove that only isomorphisms are exponentiable homomorphi...

let g be a (p, q) graph. let k be an integer with 2 ≤ k ≤ p and f from v (g) to the set {1, 2, . . . , k} be a map. for each edge uv, assign the label |f(u) − f(v)|. the function f is called a k-difference cordial labeling of g if |νf (i) − vf (j)| ≤ 1 and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labelled with x (x ∈ {1, 2 . . . , k}), ef (1) and ef (0) respectively den...

1.2. Proposition. — π : PnA → SpecA is a closed morphism. Proof. Suppose Z ↪→ PnA is a closed subset. We wish to show that π(Z) is closed. Suppose y / ∈ π(Z) is a closed point of SpecA. We’ll check that there is a distinguished open neighborhood D(f) of y in SpecA such that D(f) doesn’t meet π(Z). (If we could show this for all points of π(Z), we would be done. But I prefer to concentrate on cl...