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The monadic secondorder logic of graphs I. Recognizable sets of Finite Graphs
 Information and Computation
, 1990
"... The notion of a recognizable sef offinite graphs is introduced. Every set of finite graphs, that is definable in monadic secondorder logic is recognizable, but not vice versa. The monadic secondorder theory of a contextfree set of graphs is decidable. 0 19W Academic Press. Inc. This paper begins ..."
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Cited by 301 (17 self)
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The notion of a recognizable sef offinite graphs is introduced. Every set of finite graphs, that is definable in monadic secondorder logic is recognizable, but not vice versa. The monadic secondorder theory of a contextfree set of graphs is decidable. 0 19W Academic Press. Inc. This paper begins
On limits of finite graphs
 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 ..."
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Cited by 33 (2 self)
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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
 J. MATH. SCI. UNIV. TOKYO
, 2000
"... Poles of the Ihara zeta function associated with a finite graph are described by graphtheoretic quantities. Elementary proofs based on the notions of oriented line graphs, PerronFrobenius operators, and discrete Laplacians are provided for Bass’s theorem on the determinant expression of the zeta f ..."
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Cited by 39 (1 self)
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Poles of the Ihara zeta function associated with a finite graph are described by graphtheoretic quantities. Elementary proofs based on the notions of oriented line graphs, PerronFrobenius operators, and discrete Laplacians are provided for Bass’s theorem on the determinant expression of the zeta
The C*Algebras of rowfinite graphs
, 2000
"... We prove versions of the fundamental theorems about CuntzKrieger algebras for the C*algebras of rowfinite 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 ..."
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Cited by 88 (19 self)
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We prove versions of the fundamental theorems about CuntzKrieger algebras for the C*algebras of rowfinite 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
 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. ..."
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Cited by 43 (8 self)
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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
"... 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 ..."
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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
, 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 ..."
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Cited by 1 (0 self)
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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
kUniversal Finite Graphs
, 1996
"... This paper investigates the class of kuniversal 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 kuniversal graphs is not de nable by a ..."
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Cited by 3 (1 self)
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This paper investigates the class of kuniversal 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 kuniversal graphs is not de nable
Signless Laplacians of finite graphs
, 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 ..."
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Cited by 52 (2 self)
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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
 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. ..."
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Cited by 1200 (5 self)
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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
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6,752