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ON UNICYCLIC REFLEXIVE GRAPHS
"... A simple graph is said to be reflexive if the second largest eigenvalue of its (0,1)adjacency matrix does not exceed 2. Based on some recent results on reflexive graphs with more cycles and some new observations, we construct in this paper several classes of maximal unicyclic reflexive graphs. 1. ..."
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A simple graph is said to be reflexive if the second largest eigenvalue of its (0,1)adjacency matrix does not exceed 2. Based on some recent results on reflexive graphs with more cycles and some new observations, we construct in this paper several classes of maximal unicyclic reflexive graphs. 1.
List Homomorphisms to Reflexive Graphs
, 1998
"... Let H be a fixed graph. We introduce the following list homomorphism problem: Given an input graph G and for each vertex v of G a ``list' ' L(v) V(H), decide whether or not there is a homomorphism f:G H such that f(v)#L(v) for each v#V(G). We discuss this problem primarily in the context o ..."
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Cited by 57 (24 self)
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of reflexive graphs, i.e., graphs in which each vertex has a loop. We give a polynomial time algorithm to solve the problem when H is an interval graph and prove that when H is not an interval graph the problem is NPcomplete. If the lists are restricted to induce connected subgraphs of H, we give a polynomial
Reflexive Graphs and Parametric Polymorphism
, 1993
"... this paper is to understand why that is a parametric categorical model. In [10] Ma and Reynolds propose a parametricity hypothesis for a functor between categorical models of polymorphism which essentially requires that there is an extension of (a certain form of) an identity relation functor which ..."
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Cited by 25 (1 self)
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presented in [10] can be viewed as a "parametric completion". We shall also follow the suggestion of Ma in [9] that subtyping is a kind of parametricity requirement and show how to fit subtyping in the same setup. The basic idea is to use reflexive graphs of categories as in [12]. We shall employ
Atomic Compactness and Reflexive Graphs.
, 1996
"... A first order structure M with universe M is atomic compact if every system of atomic formulas with parameters in M is satisfiable in M provided each of its finite subsystems is. The definition of atomic compactness goes back to Weglorz [Weg]. It extends to general first order structures the notion ..."
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of equational compactness, first considered by I. Kaplansky and J. Løs for Abelian groups, and later by J. Mycielsky for general algebras (see [Myc]). We present here miscellaneous results about atomic compactness of reflexive graphs. Contents 1 Preliminaries. 2 2 Graphs. 3 2.1 Conventions
DISTRIBUTIVE LATTICE POLYMORPHISM ON REFLEXIVE GRAPHS
"... Abstract. In this paper we give two characterisations of the class of reflexive graphs admitting distributive lattice polymorphisms and use these characterisations to attack the problem of finding a polynomial time recognition algorithm for these graphs. We provide a polynomial time recognition alg ..."
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Abstract. In this paper we give two characterisations of the class of reflexive graphs admitting distributive lattice polymorphisms and use these characterisations to attack the problem of finding a polynomial time recognition algorithm for these graphs. We provide a polynomial time recognition
Special reflexive graphs in modular varieties, Algebra univers
"... Abstract. We investigate a special kind of reflexive graphs in any congruence modular variety. When the variety is Maltsev these special reflexive graphs are exactly the internal groupoids, when the variety is distributive they are the internal reflexive relations. We use these internal structures t ..."
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Abstract. We investigate a special kind of reflexive graphs in any congruence modular variety. When the variety is Maltsev these special reflexive graphs are exactly the internal groupoids, when the variety is distributive they are the internal reflexive relations. We use these internal structures
NEARUNANIMITY FUNCTIONS AND VARIETIES OF REFLEXIVE GRAPHS
, 2008
"... Let H be a graph and k ≥ 3. A nearunanimity function of arity k is a mapping g from the ktuples over V (H) toV (H) such that g(x1,x2,...,xk) is adjacent to g(x ′ 1,x ′ 2,...,x ′ k) whenever xix ′ i ∈ E(H) for each i =1, 2,...,k, and g(x1,x2,...,xk) =a whenever at least k − 1of the xi’s equal a. ..."
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Cited by 4 (2 self)
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. Feder and Vardi proved that, if a graph H admits a nearunanimity function, then the homomorphism extension (or retraction) problem for H is polynomial time solvable. We focus on nearunanimity functions on reflexive graphs. The best understood are reflexive chordal graphs H: they always admit a near
Parametricity as a Notion of Uniformity in Reflexive Graphs
, 2002
"... data types embody uniformity in the form of information hiding. Information hiding enforces the uniform treatment of those entities that dier only on hidden information. ..."
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Cited by 15 (3 self)
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data types embody uniformity in the form of information hiding. Information hiding enforces the uniform treatment of those entities that dier only on hidden information.
DOI:10.2298/FIL0903257K UNICYCLIC REFLEXIVE GRAPHS WITH SEVEN LOADED VERTICES OF THE CYCLE ∗
"... A simple graph is reflexive if the second largest eigenvalue of its (0, 1)−adjacency matrix does not exceed 2. A vertex of the cycle of unicyclic simple graph is said to be loaded if its degree is greater than 2. In this paper we establish that the length of the cycle of unicyclic reflexive graph wi ..."
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A simple graph is reflexive if the second largest eigenvalue of its (0, 1)−adjacency matrix does not exceed 2. A vertex of the cycle of unicyclic simple graph is said to be loaded if its degree is greater than 2. In this paper we establish that the length of the cycle of unicyclic reflexive graph
Results 1  10
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