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Generalization of the Bollobás-Riordan polynomial for tensor graphs
(multivariate) topological graph polynomials group eld theory
2011/1/19
Tensor models are used nowadays for implementing a fundamental theory of quan-tum gravity. We de ne here a polynomial T encoding the supplementary topological information.
The incidence Hopf algebra of graphs
combinatorial Hopf algebra graph chromatic polynomial
2011/2/24
The graph algebra is a commutative, cocommutative, graded,connected incidence Hopf algebra, whose basis elements correspond to fi-nite simple graphs and whose Hopf product and coproduct admit simple c...
Isoradial graphs are a natural generalization of regular graphs which give,for many models of statistical mechanics, the right framework for studying models at criticality.
The generalized connectivity of complete bipartite graphs
k-connectivity complete bipartite graph edge-disjoint spanning trees
2011/2/28
Let G be a nontrivial connected graph of order n, and k an integer with 2 ≤k ≤ n. For a set S of k vertices of G, let κ(S) denote the maximum number ℓ of edge-disjoint trees T1, T2, . . . , T...
The Erdős-Ko-Rado theorem for twisted Grassmann graphs
The Erd˝ os–Ko–Rado theorem Distance-regular graph Twisted Grass-mann graph
2011/2/28
We present a “modern” approach to the Erd˝os–Ko–Rado theorem for Q-polynomial distance-regular graphs and apply it to the twisted Grass-mann graphs discovered in 2005 by van Dam and Koolen.
Cohen-Macaulayness of bipartite graphs, revisited
edge ideal of a graph Cohen-Macaulay bipartite graph
2011/1/17
Cohen-Macaulayness of bipartite graphs is investigated by several mathematicians and has been characterized combinatorially. In this note, we give some different combi-natorial conditions for a bipart...
Tricyclic graphs with exactly two main eigenvalues
Main eigenvalues Tricyclic graphs 2-walk (a, b)-linear graphs
2011/1/18
An eigenvalue of a graph G is called a main eigenvalue if it has an eigenvector the sum of whose entries is not equal to zero. In this paper, all connected tricyclic graphs with exactly two main eigen...
Distance-balanced closure of some graphs
Distances in graphs distance-balanced graphs distance-balanced closure
2011/2/22
In this paper we prove that any distance-balanced graph G with (G) |V (G)| − 3 is regular. Also we define notion of distance-balanced closure of a graph and we find distance-
balanced closur...
Exponentially many perfect matchings in cubic graphs
Exponentially many perfect matchings cubic graphs
2011/1/21
We show that every cubic bridgeless graph G has at least 2|V (G)|/3656 perfect matchings.
This confirms an old conjecture of Lov´asz and Plummer.
In this paper we consider the hyperspace Cn(X) of closed, con-nected, non-empty subsets of a base space X. The class of base spaces we consider we call finite ray-graphs, and are a noncompact variatio...
Tuza conjectured that for every graph G, the maximum size of a set of edge-disjoint triangles and minimum size of a set of edges meeting all triangles, satisfy 2.
Hardness, approximability, and exact algorithms for vector domination and total vector domination in graphs
Hardness approximability exact algorithms vector domination total vector domination
2011/3/2
We consider two graph optimization problems called vector domination and total vector domination. In vector domination one seeks a small subset S of vertices of a graph such that any vertex outside S ...
We study the commutation structure within the Pauli groups built on all decompositions of a given Hilbert space dimension q, containing a square, into its factors.
Polynomial invariants of graphs on surfaces
Graphs on surfaces ribbon graphs matroids Krushkal polynomial
2011/2/25
For a graph embedded into a surface, we relate many combinatorial parameters of the cycle matroid of the graph and the bond matroid of the dual graph with the topological parameters of the embedding. ...
Minimizing Laplacian spectral radius of unicyclic graphs with fixed girth
Laplacian matrix Laplacian spectral radius girth unicyclic graph
2011/1/18
In this paper we consider the following problem: Over the class of all simple con-nected unicyclic graphs on n vertices with girth g (n, g being fixed), which graph minimizes the Laplacian spectral ra...