Graph homomorphism has been studied intensively. Given an m ×m symmetric matrix A, the graph homomorphism function is defined as

1. I n t r o d u c t i o n 1. Let M be a real-analytic manifold, Vect M the Lie algebra of analytic vector fields on M. We consider a vector field f E Vect M as a differential operator of first order on the algebra of smooth functions C ~ (M) which satisfies the differentiation rule f(W1W2) -" (fw1)W2 + wI(fW2) VWI, W2 E Coo(M). A point z E M will be identified with the corresponding homomorphi...

A homomorphism from an oriented graph G to an oriented graph H is an arc-preserving mapping φ from V (G) to V (H), that is φ(x)φ(y) is an arc in H whenever xy is an arc in G. The oriented chromatic number of G is the minimum order of an oriented graph H such that G has a homomorphism to H . The oriented chromatic index of G is the minimum order of an oriented graph H such that the line-digraph ...

For a fixed oriented tree T, we consider the complexity of deciding whether or not a given digraph G is homomorphic to T. It was shown by Gutjahr, Woeginger and Welzl that there exist trees T for which this homomorphism problem is NP-complete. However, it seems difficult to decide just which trees T yield NP-complete homomorphism problems. In this paper, we first identify a class of simple tree...

We introduce a notion of an integral along bimonoid homomorphism as simultaneous generalization the and cointegral bimonoids. The purpose this paper is to characterize existence specific integral, called normalized generator in terms kernel cokernel homomorphism. volume on abelian category dimension vector spaces order groups. In applications, we show that there exists nontrivial partially defi...

this paper continues the investigation of the rst author begun in part one. the hereditary properties of n-homomorphism amenability for banach algebras are investigated and the relations between n-homomorphism amenability of a banach algebra and its ide- als are found. analogous to the character amenability, it is shown that the tensor product of two unital banach algebras is n-homomorphism am...

We initiate a study of the homomorphism domination exponent of a pair of graphs F and G, defined as the maximum real number c such that |Hom(F, T )| > |Hom(G,T )| for every graph T . The problem of determining whether HDE(F,G) > 1 is known as the homomorphism domination problem and its decidability is an important open question arising in the theory of relational databases. We investigate the c...

We prove the generalized Hyers--Ulam stability  of $n$-th order linear differential equation of the form $$y^{(n)}+p_{1}(x)y^{(n-1)}+ cdots+p_{n-1}(x)y^{prime}+p_{n}(x)y=f(x),$$ with condition that there exists a non--zero solution of corresponding homogeneous equation. Our main results extend and improve the corresponding results obtained by many authors.

Let G and H be two groups. For simplicity, we denote by + the group operation in each of these groups. A function f : G → H is called a (group) homomorphism if for every x, y ∈ G it holds that f(x+ y) = f(x) + f(y). One important special case of interest is when H is a finite field and G is a vector space over this field; that is, G = H for some natural number m. In this case, a homomorphism f ...

We prove that if G and H are primitive strongly regular graphs with the same parameters and φ is a homomorphism from G to H, then φ is either an isomorphism or a coloring (homomorphism to a complete subgraph). Moreover, any such coloring is optimal for G and its image is a maximum clique of H. Therefore, the only endomorphisms of a primitive strongly regular graph are automorphisms or colorings...