Results 1 - 10 of 6,752

The monadic second-order logic of graphs I. Recognizable sets of Finite Graphs

by Bruno Courcelle - Information and Computation , 1990
"... The notion of a recognizable sef offinite graphs is introduced. Every set of finite graphs, that is definable in monadic second-order logic is recognizable, but not vice versa. The monadic second-order theory of a context-free set of graphs is decidable. 0 19W Academic Press. Inc. This paper begins ..."
Abstract - Cited by 301 (17 self) - Add to MetaCart
The notion of a recognizable sef offinite graphs is introduced. Every set of finite graphs, that is definable in monadic second-order logic is recognizable, but not vice versa. The monadic second-order theory of a context-free set of graphs is decidable. 0 19W Academic Press. Inc. This paper begins

On limits of finite graphs

by Gábor Elek - Combinatorica
"... Abstract. We prove that for any weakly convergent sequence of finite graphs with bounded vertex degrees, there exists a topological limit graphing. AMS Subject Classifications: 05C80 ..."
Abstract - Cited by 33 (2 self) - Add to MetaCart
Abstract. We prove that for any weakly convergent sequence of finite graphs with bounded vertex degrees, there exists a topological limit graphing. AMS Subject Classifications: 05C80

Zeta functions of finite graphs

by Motoko Kotani, Toshikazu Sunada - J. MATH. SCI. UNIV. TOKYO , 2000
"... Poles of the Ihara zeta function associated with a finite graph are described by graph-theoretic quantities. Elementary proofs based on the notions of oriented line graphs, Perron-Frobenius operators, and discrete Laplacians are provided for Bass’s theorem on the determinant expression of the zeta f ..."
Abstract - Cited by 39 (1 self) - Add to MetaCart
Poles of the Ihara zeta function associated with a finite graph are described by graph-theoretic quantities. Elementary proofs based on the notions of oriented line graphs, Perron-Frobenius operators, and discrete Laplacians are provided for Bass’s theorem on the determinant expression of the zeta

The C*-Algebras of row-finite graphs

by Teresa Bates, David Pask, Iain Raeburn, Wojciech Szymanski , 2000
"... We prove versions of the fundamental theorems about Cuntz-Krieger algebras for the C*-algebras of row-finite graphs: directed graphs in which each vertex emits at most finitely many edges. Special cases of these results have previously been obtained using various powerful machines; our main point is ..."
Abstract - Cited by 88 (19 self) - Add to MetaCart
We prove versions of the fundamental theorems about Cuntz-Krieger algebras for the C*-algebras of row-finite graphs: directed graphs in which each vertex emits at most finitely many edges. Special cases of these results have previously been obtained using various powerful machines; our main point

Quantum automorphism groups of finite graphs

by Julien Bichon - Proc. Amer. Math. Soc. 131 (2003), 665–673. TEODOR BANICA AND JULIEN BICHON
"... Abstract. We determine the quantum automorphism groups of finite graphs. These are quantum subgroups of the quantum permutation groups defined by Wang. The quantum automorphism group is a stronger invariant for finite graphs than the usual automorphism group. We get a quantum dihedral group D4. 1. ..."
Abstract - Cited by 43 (8 self) - Add to MetaCart
Abstract. We determine the quantum automorphism groups of finite graphs. These are quantum subgroups of the quantum permutation groups defined by Wang. The quantum automorphism group is a stronger invariant for finite graphs than the usual automorphism group. We get a quantum dihedral group D4. 1.

Modal Logics for Finite Graphs

by Mario Benevides, Depart Ciencia
"... In this work, we present modal logics for four classes of finite graphs: finite direct graphs, finite acyclic direct graphs, finite undirect graphs, finite irreflexive undirect graphs. For all these modal proof theory we prove soundness and completeness with respect to one of these classes of graphs ..."
Abstract - Add to MetaCart
In this work, we present modal logics for four classes of finite graphs: finite direct graphs, finite acyclic direct graphs, finite undirect graphs, finite irreflexive undirect graphs. For all these modal proof theory we prove soundness and completeness with respect to one of these classes

Percolation on finite graphs

by Itai Benjamini , 2001
"... Several questions and few answers regarding percolation on finite graphs are presented. The following is a note regarding the asymptotic study of percolation on finite transitive graphs. On the one hand, the theory of percolation on infinite graphs is rather developed, although still with many open ..."
Abstract - Cited by 1 (0 self) - Add to MetaCart
Several questions and few answers regarding percolation on finite graphs are presented. The following is a note regarding the asymptotic study of percolation on finite transitive graphs. On the one hand, the theory of percolation on infinite graphs is rather developed, although still with many open

k-Universal Finite Graphs

by Eric Rosen, Saharon Shelah, Scott Weinstein , 1996
"... This paper investigates the class of k-universal finite graphs, a local analog of the class of universal graphs, which arises naturally in the study of finite variable logics. The main results of the paper, which are due to Shelah, establish that the class of k-universal graphs is not de nable by a ..."
Abstract - Cited by 3 (1 self) - Add to MetaCart
This paper investigates the class of k-universal finite graphs, a local analog of the class of universal graphs, which arises naturally in the study of finite variable logics. The main results of the paper, which are due to Shelah, establish that the class of k-universal graphs is not de nable

Signless Laplacians of finite graphs

by Dragos Cvetković , 2006
"... Let G be a simple graph with n vertices. The characteristic polynomial det(xI − A) of a (0,1)-adjacency matrix A of G is called the characteristic polynomial of G and denoted by PG(x). The eigenvalues of A (i.e. the zeros of det(xI − A)) and the spectrum of A (which consists of the n eigenvalues) ar ..."
Abstract - Cited by 52 (2 self) - Add to MetaCart
with respect to M. A graph H cospectral with a graph G, but not isomorphic to G, is called a cospectral mate of G. Let G be a finite set of graphs. Let G ′ be the set of graphs in G which have a cospectral mate in G with respect to an associated matrix M. The ratio |G ′ |/|G | is called the spectral

Graph Theory

by Reinhard Diestel , Alexander Schrijver , Paul D. Seymour - MATHEMATISCHES FORSCHUNGSINSTITUT OBERWOLFACH REPORT NO. 16/2007 , 2007
"... This week broadly targeted both finite and infinite graph theory, as well as matroids, including their interaction with other areas of pure mathematics. The talks were complemented by informal workshops focussing on specific problems or particularly active areas. ..."
Abstract - Cited by 1200 (5 self) - Add to MetaCart
This week broadly targeted both finite and infinite graph theory, as well as matroids, including their interaction with other areas of pure mathematics. The talks were complemented by informal workshops focussing on specific problems or particularly active areas.
Results 1 - 10 of 6,752