Representation theorems for graphs whose the vertex set is partially ordered

Some Representation Theorems for Partially Ordered Sets

Ordering Subsets of (partially) Ordered Sets: Representation Theorems

In many practical situations, we have a (partially) ordered set V of different values. For example, we may have the set of all possible values of temperature, or the set of all possible degrees of confidence in a statement. In practice, we are often uncertain about the exact value of the quantity. Due to this uncertainty, at best, we know a set S ⊆ V of possible values of the quantity: e.g., an...

Morita theorems for partially ordered monoids

Two partially ordered monoids S and T are called Morita equivalent if the categories of right S-posets and right T -posets are Pos-equivalent as categories enriched over the category Pos of posets. We give a description of Pos-prodense biposets and prove Morita theorems I, II, and III for partially ordered monoids.

Sampling of Multiple Variables Based on Partially Ordered Set Theory

We introduce a new method for ranked set sampling with multiple criteria. The method relaxes the restriction of selecting just one individual variable from each ranked set. Under the new method for ranking, units are ranked in sets based on linear extensions in partially order set theory with considering all variables simultaneously. Results willbe evaluated by a relatively extensive simulation...

On vertex balance index set of some graphs

Let Z2 = {0, 1} and G = (V ,E) be a graph. A labeling f : V → Z2 induces an edge labeling f* : E →Z2 defined by f*(uv) = f(u).f (v). For i ε Z2 let vf (i) = v(i) = card{v ε V : f(v) = i} and ef (i) = e(i) = {e ε E : f*(e) = i}. A labeling f is said to be Vertex-friendly if | v(0) − v(1) |≤ 1. The vertex balance index set is defined by {| ef (0) − ef (1) | : f is vertex-friendly}. In this paper ...