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Complexes of not iconnected graphs
 TOPOLOGY
, 1999
"... Complexes of (not) connected graphs, hypergraphs and their homology appear in the construction of knot invariants given by V. Vassiliev [V1, V2, V3]. In this paper we study the complexes of not iconnected khypergraphs on n vertices. We show that the complex of not 2connected graphs has the homot ..."
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Cited by 21 (1 self)
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Complexes of (not) connected graphs, hypergraphs and their homology appear in the construction of knot invariants given by V. Vassiliev [V1, V2, V3]. In this paper we study the complexes of not iconnected khypergraphs on n vertices. We show that the complex of not 2connected graphs has
A RESULT ON CONNECTED GRAPHS
"... The field of mathematics plays very important role in different fields. One of the important areas in mathematics is graph theory which is used in structural models. This structural preparations of various objects or technologies direct to new inventions and modifications in the existing environment ..."
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environment for development in those fields. The field graph theory started its journey from the problem of Konigsberg bridge in 1735.In this paper we discuss Graphs, vertices and edges, connected graph and relation between connected graphs, edges.
Smoothed analysis on connected graphs
, 2013
"... The main paradigm of smoothed analysis on graphs suggests that for any large graph G in a certain class of graphs, perturbing slightly the edges of G at random (usually adding few random edges to G) typically results in a graph having much “nicer ” properties. In this work we study smoothed analysis ..."
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analysis on trees or, equivalently, on connected graphs. Given an nvertex connected graph G, form a random supergraph G ∗ of G by turning every pair of vertices of G into an edge with probability εn, where ε is a small positive constant. This perturbation model has been studied previously in several
On k–Chromatically Connected Graphs
"... A graph G is chromatically k–connected if every vertex cutset induces a subgraph with chromatic number at least k. Thus, in particular each neighborhood has to induce a k–chromatic subgraph. In [3], Godsil, Nowakowski and Nešetřil asked whether there exists a k–chromatically connected graph such ..."
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A graph G is chromatically k–connected if every vertex cutset induces a subgraph with chromatic number at least k. Thus, in particular each neighborhood has to induce a k–chromatic subgraph. In [3], Godsil, Nowakowski and Nešetřil asked whether there exists a k–chromatically connected graph
Strongly connected graphs and polynomials
, 2011
"... In this report, we give the exact solutions ofthe equation P(A) = 0 where P is a polynomial of degree2 with integer coefficients, and A is the adjacency matrix of a strongly connected graph. Then we study the problem for P a polynomial of degree n ≥ 3, and give a necessary condition on the trace of ..."
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In this report, we give the exact solutions ofthe equation P(A) = 0 where P is a polynomial of degree2 with integer coefficients, and A is the adjacency matrix of a strongly connected graph. Then we study the problem for P a polynomial of degree n ≥ 3, and give a necessary condition on the trace
The cyclomatic number of connected graphs
, 2012
"... We study the combinatorics of constructing nonsingular geometrically irreducible projective curves that do not admit rational points over finite solvable extensions of the base field. A graph is without solvable orbits if its group of automorphisms acts on each of its orbits through a nonsolvabl ..."
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solvable quotient. We prove that there is a connected graph without solvable orbits of cyclomatic number c if and only if c is equal
Growing wellconnected graphs
, 2006
"... The algebraic connectivity of a graph is the second smallest eigenvalue of the graph Laplacian, and is a measure of how wellconnected the graph is. We study the problem of adding edges (from a set of candidate edges) to a graph so as to maximize its algebraic connectivity. This is a difficult comb ..."
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Cited by 56 (1 self)
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The algebraic connectivity of a graph is the second smallest eigenvalue of the graph Laplacian, and is a measure of how wellconnected the graph is. We study the problem of adding edges (from a set of candidate edges) to a graph so as to maximize its algebraic connectivity. This is a difficult
Counting Connected Graphs Asymptotically
, 2008
"... We find the asymptotic number of connected graphs with k vertices and k − 1 + l edges when k, l approach infinity, reproving a result of Bender, Canfield and McKay. We use the probabilistic method, analyzing breadthfirst search on the random graph G(k, p) for an appropriate edge probability p. Cent ..."
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Cited by 5 (0 self)
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We find the asymptotic number of connected graphs with k vertices and k − 1 + l edges when k, l approach infinity, reproving a result of Bender, Canfield and McKay. We use the probabilistic method, analyzing breadthfirst search on the random graph G(k, p) for an appropriate edge probability p
Results 1  10
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688,505