Let K and L be lattices, and let φ be a homomorphism of K into L. Then φ induces a natural 0-preserving join-homomorphism of ConK into ConL. Extending a result of A. Huhn, the authors proved that if D and E are finite distributive lattices and ψ is a 0-preserving join-homomorphism from D into E, then D and E can be represented as the congruence lattices of the finite lattices K and L, respectiv...

We show that the 2-edge-colored chromatic number of a class of simple graphs is bounded if and only if the acyclic chromatic number is bounded for this class. Recently, the CSP dichotomy conjecture has been reduced to the case of 2-edge-colored homomorphism and to the case of 2-vertex-colored homomorphism. Both reductions are rather long and follow the reduction to the case of oriented homomorp...

If (R,M) and (S,N) are quasilocal (commutative integral) domains and f : R → S is a (unital) ring homomorphism, then f is said to be a strong local homomorphism (resp., radical local homomorphism) if f (M) = N (resp., f (M) ⊆ N and for each x ∈ N , there exists a positive integer t such that xt ∈ f (M)). It is known that if f : R→ S is a strong local homomorphism where R is a pseudovaluation do...

For digraphs G and H, a homomorphism of G to H is a mapping f : V (G)→V (H) such that uv ∈ A(G) implies f(u)f(v) ∈ A(H). If, moreover, each vertex u ∈ V (G) is associated with costs ci(u), i ∈ V (H), then the cost of a homomorphism f is ∑ u∈V (G) cf(u)(u). For each fixed digraph H, the minimum cost homomorphism problem for H, denoted MinHOM(H), can be formulated as follows: Given an input digra...

In this paper we find a secure routing protocol for computer networks, which finds minimum optimum path using homomorphic encryption schemes. We briefly look into the existing homomorphic encryption algorithms. We make use of ElGamal encryption, Elliptic Curve encryption and a privacy homomorphism, which exhibits the property of homomorphism in our new routing protocol. Elliptic curve exhibits ...

In this paper, we introduce the concept of an M-fuzzy subgroup of an M-group and discussed some of its properties.

where (x, g) denotes % evaluated at g. Each % thus yields a homomorphism of M(G) onto the complex numbers. Every such homomorphism of L(G) is obtained in this way. Let be a homomorphism of L{G) into M(H). After composing with <[>, every homomorphism of M(H) onto the complex numbers either is identically zero, or can be identified with a member of G. We thus have a map <£* from Ê into {G, 0 ...

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 problem was motivated by a realworld problem in defence logistics and was introduced in ...

For digraphs G and H , a homomorphism of G to H is a mapping f : V (G)→V (H) such that uv ∈ A(G) implies f(u)f(v) ∈ A(H). If, moreover, each vertex u ∈ V (G) is associated with costs ci(u), i ∈ V (H), then the cost of a homomorphism f is ∑ u∈V (G) cf(u)(u). For each fixed digraph H , the minimum cost homomorphism problem for H , denoted MinHOM(H), can be formulated as follows: Given an input di...