Let Γ be a graph and let G be a group of automorphisms of Γ. The graph Γ is called G-normal if G is normal in the automorphism group of Γ. Let T be a finite non-abelian simple group and let G = T l with l ≥ 1. In this paper we prove that if every connected pentavalent symmetric T -vertex-transitive graph is T -normal, then every connected pentavalent symmetric G-vertex-transitive graph is G-nor...

We investigate the expressive power of fragments of rst-order logic that are deened in terms of preexes. The main result establishes a strict hierarchy among these fragments over the signature consisting of a single binary relation. It implies that for each preex p, there is a sentence ' p in prenex normal form with preex p, over a single binary relation, such that for all sentences in prenex n...

Normal graphs are defined in terms of cross-intersecting set families: a graph is normal if it admits a clique cover Q and a stable set cover S s.t. every clique in Q intersects every stable set in S. Normal graphs can be considered as closure of perfect graphs by means of co-normal products (K ̈orner [6]) and graph entropy (Czisz ́ar et al. [5]). Perfect graphs have been recently characterized a...

This paper continues the line of research on the representation and compilation of propositional knowledge bases with propositional directed acyclic graphs (PDAG), negation normal forms (NNF), and binary decision diagrams (BDD). The idea is to permit variables with more than two states and to explicitly represent them in their most natural way. The resulting representation languages are analyze...

let $r$ be a commutative ring with identity. let $g(r)$ denote the maximal graph associated to $r$, i.e., $g(r)$ is a graph with vertices as the elements of $r$, where two distinct vertices $a$ and $b$ are adjacent if and only if there is a maximal ideal of $r$ containing both. let $gamma(r)$ denote the restriction of $g(r)$ to non-unit elements of $r$. in this paper we study the various graphi...

A homogeneous graph is a graph together with a group which acts transitively on vertices as symmetries of the graph. We consider Laplacians of homogeneous graphs and generalizations of Laplacians whose eigenvalues can be associated with various equilibria of forces in molecules (such as vibrational modes of buckyballs). Methods are given for calculating such eigenvalues by combining concepts an...

We derive several algorithms for curves and surfaces represented using normal coordinates. The normal coordinate representation is a very succinct representation of curves and surfaces. For embedded curves, for example, its size is logarithmically smaller than a representation by edge intersections in a triangulation. Consequently, fast algorithms for normal representations can be exponentially...

A control flow graph represents all the flows of control that may arise during program execution. Since exception mechanism in Java induces flows of control, exception induced control flow have to be incorporated in control flow graph. In the previous research to construct control flow graph, they compute exception flow and normal flow at the same time while computing control flow information. ...

In this paper we relate antiblocker duality between polyhedra, graph theory and the disjunctive procedure. In particular, we analyze the behavior of the disjunctive procedure over the clique relaxation, K(G), of the stable set polytope in a graph G and the one associated to its complementary graph, K(Ḡ). We obtain a generalization of the Perfect Graph Theorem proving that the disjunctive indice...