Related papers: On partial endomorphisms of a star graph
A star coloring of a graph $G$ is a proper coloring where vertices of every two color classes induce a forest of stars. A strict partial order is defined on the set of all star colorings of $G$. We introduce the star b-chromatic number…
Monoids and groupoids are examples of poloids. On the one hand, poloids can be regarded as one-sorted categories; on the other hand, poloids can be represented by partial magmas of partial transformations. In this article, poloids are…
Given the action of a group $G$ on a set $X$, an endomorphism of $X$ is a function $f:X \rightarrow X$ which is $G$-equivariant, that is, it commutes with the action, i.e., $f(g\cdot x)= g\cdot f(x)$, for all $x\in X$. The set of…
In this partly expository paper we discuss and describe some of our old and recent results on partial orders on the set (m,n)-graphs (i.e. graphs with n vertices and m edges) and some operations on graphs that are monotone with respect to…
We classify the $\mathscr{R}$-cross-sections of the monoid of order-preserving transformations on the $n$-element chain in terms of certain binary trees.
We introduce a new notation for representing labeled regular bipartite graphs of arbitrary degree. Several enumeration problems for labeled and unlabeled regular bipartite graphs have been introduced. A general algorithm for enumerating all…
The monoids of simplicial endomorphisms, i.e. the monoids of endomorphisms in the simplicial category, are submonoids of monoids one finds in Temperley-Lieb algebras, and as the monoids of Temperley-Lieb algebras are linked to situations…
Each finite and connected bipartite graph induces a finite collection of non-isomorphic dessins d'enfants, that is, $2$-cell embeddings of it into some closed orientable surface. We describe an algorithm to compute all these dessins…
For a given graph consider a pair of disjoint matchings the union of which contains as many edges as possible. Furthermore, consider the relation of the cardinalities of a maximum matching and the largest matching in those pairs. It is…
Let ${\cal I}_n$ be the symmetric inverse semigroup on $X_n = \{1, 2,..., n\}$ and let ${\cal DP}_n$ and ${\cal ODP}_n$ be its subsemigroups of partial isometries and of order-preserving partial isometries of $X_n$, respectively. In this…
In this paper we determine the exact values of the signed domination number, signed total domination number, and minus domination number of complete multipartite graphs, which substantially generalizes some previous results obtained for…
We investigate topological, combinatorial, statistical, and enumeration properties of finite graphs with high Kolmogorov complexity (almost all graphs) using the novel incompressibility method. Example results are: (i) the mean and variance…
Let M be a monoidal category endowed with a distinguished class of weak equivalences and with appropriately compatible classifying bundles for monoids and comonoids. We define and study homotopy-invariant notions of normality for maps of…
For a group $G$ acting over a set $X$, the set of all the $G$-equivariant functions, i.e., the set of functions which conmute with the action, ($g\cdot f(x)=g\cdot f(x), \forall g\in G, \forall x\in X$), is a monoid with the composition.…
We provide a complete system of invariants for the formal classification of complex analytic unipotent germs of diffeomorphism at $\cn{n}$ fixing the orbits of a regular vector field. We reduce the formal classification problem to solve a…
We present simple graph-theoretic characterizations of Cayley graphs for left-cancellative monoids, groups, left-quasigroups and quasigroups. We show that these characterizations are effective for the end-regular graphs of finite degree.
The algebraic monoid structure of an incidence algebra is investigated. We show that the multiplicative structure alone determines the algebra automorphisms of the incidence algebra. We present a formula that expresses the complexity of the…
The aim of the paper is to give a full classification of factorizations of groups in terms of descent cohomology (pointed) sets introduced in [5]. We show that descent cohomology includes Serre's non-abelian group cohomology as a special…
Let A^2 denote the affine plane over an algebraically closed field of arbitrary characteristic. Besides contributing several new results in the general theory of birational endomorphisms of A^2, this article describes certain classes of…
We study the problem of finding the minimal (maximal) genus for a surface where a given four-valent graph with fixed opposite edge structure can be embedded into. We find several partial relations and give new reformulations in…