For digraphs D and H , a mapping f : V (D) → V (H) is a homomorphism of D to H if uv ∈ A(D) implies f (u)f (v) ∈ A(H). For a fixed digraph H , the homomorphism problem is to decide whether an input digraph D admits a homomorphism to H or not, and is denoted as HOM(H). An optimization version of the homomorphism problemwasmotivated by a real-world problem in defence logistics and was introduced ...

(a) Describe the conjugacy classes of D and use this to prove that D is simple. [Hint: Any normal subgroup is a union of conjugacy classes.] (b) Compute the number of distinguishable ways to color the faces of a dodecahedron with k colors. [Hint: Let X be the set of all colorings, so that |X| = k12. Many of these colorings are indistinguishable after rotation so we really want to know the numbe...

A bstract We study the perturbative structure of threshold enhanced logarithms in coefficient functions deep inelastic scattering (DIS) and semi-inclusive e + ? annihilation (SIA) processes setup a framework to sum them up all orders perturbation theory. Threshold show as distributions ((1 ?z ) 1 log i (1 )) from soft plus virtual (SV) next SV (NSV) contributions. use Sudakov differential renor...

The purpose of this experiment was to study sequential histogenesis of colonic epithelial tumours in the dimethylhydrazine (DMH) induced rat colon cancer model. Seventy outbred female Wistar rats treated with DMH (40 mg/kg, subcutaneously weekly for five weeks) were killed and autopsied in batches of 10 every five weeks from the 10th to 40th weeks from first treatment. The resulting 378 colonic...

1. Abstract characterization of Dn The group Dn has two generators r and s with orders n and 2 such that srs−1 = r−1. We will show any group with a pair of generators like r and s (except for their order) admits a homomorphism onto it from Dn, and is isomorphic to Dn if it has the same size as Dn. Theorem 1.1. Let G be generated by elements a and b where an = 1 for some n ≥ 3, b2 = 1, and bab−1...

In this paper, we define some new homomorphism-monotone parameters for hypergraphs. Using these parameters, we extend some graph homomorphism results to hypergraph case. Also, we present some bounds for some well-known invariants of hypergraphs such as fractional chromatic number,independent numer and some other invariants of hyergraphs, in terms of these parameters.

In this paper, a new concept of anti-homomorphism between two fuzzy groups G and G‫׀‬ is defined many results analogous to homomorphism of groups are established

For digraphs D and H , a mapping f : V (D)→V (H) is a homomorphism of D to H if uv ∈ A(D) implies f (u) f (v) ∈ A(H). If, moreover, each vertex u ∈ V (D) is associated with costs ci (u), i ∈ V (H), then the cost of the homomorphism f is ∑ u∈V (D) c f (u)(u). For each fixed digraph H , we have the minimum cost homomorphism problem for H (abbreviated MinHOM(H )). The problem is to decide, for an ...

Homomorphism complexes were introduced by Lovász to study topological obstructions to graph colorings. We show that folding in the second parameter of the homomorphism complex yields a homotopy equivalence. We study how the Mycielski construction changes the homotopy type of the homomorphism complex. We construct graphs showing that the topological bound obtained by odd cycles can be arbitraril...