The Endomorphism Monoids of (n − 3)-regular Graphs of Order n

This paper is motivated by the result of W. Li, he presents an infinite family of graphs - complements of cycles - which possess a regular monoid. We show that these regular monoids are completely regular. Furthermore, we characterize the regular, orthodox and completely regular endomorphisms of the join of complements of cycles, i.e. (n−3)-regular graph of order n

The endomorphisms monoids of graphs of order n with a minimum degree n − 3

We characterize the endomorphism monoids, End(G), of the generalized graphs G of order n with a minimum degree n − 3. Criteria for regularity, orthodoxy and complete regularity of those monoids based on the structure of G are given

Cores and Compactness of Infinite Directed Graphs

AbstractIn this paper we define the property of homomorphic compactness for digraphs. We prove that if a digraphHis homomorphically compact thenHhas a core, although the converse does not hold. We also examine a weakened compactness condition and show that when this condition is assumed, compactness is equivalent to containing a core. We use this result to prove that if a digraphHof sizeκis not compact, then there is a digraphGof size at mostκ+such thatHis not compact with respect toG. We then give examples of some sufficient conditions for compactness

Graphs with regular monoids

AbstractThis paper is motivated by an open question: which graphs have a regular (endomorphism) monoid? We present an infinite family of graphs, which possess a regular monoid; we also give an approach to construct a nontrivial graph of any order with this property based on a known one, by which the join of two trees with a regular monoid is explicitly described

Incidence Hypergraphs: Box Products & the Laplacian

The box product and its associated box exponential are characterized for the categories of quivers (directed graphs), multigraphs, set system hypergraphs, and incidence hypergraphs. It is shown that only the quiver case of the box exponential can be characterized via homs entirely within their own category. An asymmetry in the incidence hypergraphic box product is rectified via an incidence dual-closed generalization that effectively treats vertices and edges as real and imaginary parts of a complex number, respectively. This new hypergraphic box product is shown to have a natural interpretation as the canonical box product for graphs via the bipartite representation functor, and its associated box exponential is represented as homs entirely in the category of incidence hypergraphs; with incidences determined by incidence-prism mapping. The evaluation of the box exponential at paths is shown to correspond to the entries in half-powers of the oriented hypergraphic signless Laplacian matrix.Comment: 34 pages, 23 figures, 4 table

Graph Relations and Constrained Homomorphism Partial Orders

We consider constrained variants of graph homomorphisms such as embeddings, monomorphisms, full homomorphisms, surjective homomorpshims, and locally constrained homomorphisms. We also introduce a new variation on this theme which derives from relations between graphs and is related to multihomomorphisms. This gives a generalization of surjective homomorphisms and naturally leads to notions of R-retractions, R-cores, and R-cocores of graphs. Both R-cores and R-cocores of graphs are unique up to isomorphism and can be computed in polynomial time. The theory of the graph homomorphism order is well developed, and from it we consider analogous notions defined for orders induced by constrained homomorphisms. We identify corresponding cores, prove or disprove universality, characterize gaps and dualities. We give a new and significantly easier proof of the universality of the homomorphism order by showing that even the class of oriented cycles is universal. We provide a systematic approach to simplify the proofs of several earlier results in this area. We explore in greater detail locally injective homomorphisms on connected graphs, characterize gaps and show universality. We also prove that for every $d\geq 3$ the homomorphism order on the class of line graphs of graphs with maximum degree $d$ is universal

Matemaatika- ja mehhaanika-alaseid töid. Monoids, rings and algebras = Труды по математике и механике. Моноиды, кольца и алгебры

• М. Абель. Проективные пределы алгебр Гельфанда-Мазура • Resümee • Summary • J. Ahsаn. Hereditary and cohereditary S-sets • Resümee • Резюме • В. Бовди. Об FC-подгруппе мультипликативной группы скрещенной групповой алгебры • Resümee • Summary • К. Kaarli. On affine complete varieties generated by hemiprimal algebras with Boolean congruence lattices • Resümee • Резюме • У. Кальюлайд. Перебрасываемые элементы групповых колец • Resümee • Summary • R. Kaschek. A characterization of the principally weakly injectivity of the wreath product of acts • Resümee • Резюме • M. Кilp. Wreath products of acts over /monoids: IV. Principally weakly flat acts • Resümee • Резюме • А.Кокк. Совместный спектр и продолжение гомоморфизмов • Resümee • Summary • Р. Nогmak. РР endomorphism monoids of acts • Resümee • Резюме • У. Нуммерт. Моноиды строгих эндоморфизмов обобщенных лексикографических произведений графов • Resümee • Summary • Rämmer. On even doubly stochastic matrices with minimal even permanent • Resümee • Резюме • A. Сакс. k- сбалансированные кольца • Resümee • Summary • T. Tамме. Два несравнимых множества, инвариантные относительно группы автоморфизмов вычислительной структуры • Resümee • Summary • У.У. Умирбаев. Об аппроксимации свободных алгебр Ли относительно вхождения • Resümee • Summary • В. Фляйшер. Изоморфизм сплетений моноидов с категориями • Resümee • Summary • Я. Xион. О двусторонних сплетениях категорий • Resümee • Summary • B.П. Чуваков. О двух классах правоальтернативных колец • Resümee • Summary • Содержание. Contents • Resümeed • Summarieshttp://tartu.ester.ee/record=b1101089~S1*es