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128
Forbidden subgraphs in connected graphs
, 2004
"... Given a set ξ = {H1,H2, · · ·} of connected non acyclic graphs, a ξfree graph is one which does not contain any member of ξ as copy. Define the excess of a graph as the difference between its number of edges and its number of vertices. Let Wk,ξ be theexponential generating function (EGF for brie ..."
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Given a set ξ = {H1,H2, · · ·} of connected non acyclic graphs, a ξfree graph is one which does not contain any member of ξ as copy. Define the excess of a graph as the difference between its number of edges and its number of vertices. Let Wk,ξ be theexponential generating function (EGF
Closure and forbidden pairs for 2factors
, 2010
"... Pairs of connected graphs X, Y such that a graph G being 2connected and XYfree implies G is hamiltonian were characterized by Bedrossian. Using the closure concept for clawfree graphs, the first author simplified the characterization by showing that if considering the closure of G, the list in th ..."
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Pairs of connected graphs X, Y such that a graph G being 2connected and XYfree implies G is hamiltonian were characterized by Bedrossian. Using the closure concept for clawfree graphs, the first author simplified the characterization by showing that if considering the closure of G, the list
Efficient Algorithms for Computing All Low st Edge Connectivities and Related
 Problems, Proc. of the 18th Annual ACMSIAM Symposium on Discrete Algorithms
, 2007
"... Given an undirected unweighted graph G =(V,E) andan integer k ≥ 1, we consider the problem of computing the edge connectivities of all those (s, t) vertex pairs, whose edge connectivity is at most k. We present an algorithm with expected running time Õ(m + nk3) for this problem, where V  = n and ..."
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Cited by 7 (0 self)
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Given an undirected unweighted graph G =(V,E) andan integer k ≥ 1, we consider the problem of computing the edge connectivities of all those (s, t) vertex pairs, whose edge connectivity is at most k. We present an algorithm with expected running time Õ(m + nk3) for this problem, where V  = n
EQUIENERGETIC GRAPHS
 KRAGUJEVAC J. MATH. 26 (2004) 5–13.
, 2004
"... The energy of a graph is the sum of the absolute values of its eigenvalues. Two graphs are said to be equienergetic if their energies are equal. We show how infinitely many pairs of equienergetic graphs can be constructed, such that these graphs are connected, possess equal number of vertices, equa ..."
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Cited by 16 (4 self)
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The energy of a graph is the sum of the absolute values of its eigenvalues. Two graphs are said to be equienergetic if their energies are equal. We show how infinitely many pairs of equienergetic graphs can be constructed, such that these graphs are connected, possess equal number of vertices
On the separability of graphs
"... Abstract Recently, Cicalese and Milanič introduced a graphtheoretic concept called separability. A graph is said to be kseparable if any two nonadjacent vertices can be separated by the removal of at most k vertices. The separability of a graph G is the least k for which G is kseparable. In this ..."
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separable. In this paper, we investigate this concept under the following three aspects. First, we characterize the graphs for which in any noncomplete connected induced subgraph the connectivity equals the separability, socalled separabilityperfect graphs. We list the minimal forbidden induced subgraphs
Undirected connectivity of sparse yao graphs
 In Proceedings of the 7th ACM SIGACT/SIGMOBILE International Workshop on Foundations of Mobile Computing (FOMC 2011
, 2011
"... Given a finite set S of points in the plane and a real value d> 0, the d−radius disk graph Gd contains all edges connecting pairs of points in S that are within distance d of each other. For a given graph G with vertex set S, the Yao subgraph Yk[G] with integer parameter k> 0 contains, for e ..."
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Given a finite set S of points in the plane and a real value d> 0, the d−radius disk graph Gd contains all edges connecting pairs of points in S that are within distance d of each other. For a given graph G with vertex set S, the Yao subgraph Yk[G] with integer parameter k> 0 contains
THE ENTIRE GRAPH OF A BRIDGELESS CONNECTED PLANE GRAPH IS PANCONNECTED
"... Recently A. M. Hobbs and J. Mitchem [7] proved that the entire graph of a bridgeless connected plane graph is Hamiltonian. In this paper we strengthen this result substantially by showing that entire graphs of such plane graphs are panconnected. (Between each pair of distinct vertices in a panconnec ..."
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panconnected graph there exist paths of all lengths greater than or equal to the distance between the vertices.) This fits a pattern which indicates that Hamiltonianconnected graphs seem to have paths of " many " lengths between each pair of distinct points [1,2, 3]. The graphs we consider
Computing person and firm effects using linked longitudinal employeremployee data,” Center for Economic Studies, US Census Bureau,
, 2002
"... Abstract In this paper we provide the exact formulas for the direct least squares estimation of statistical models that include both person and firm effects. We also provide an algorithm for determining the estimable functions of the person and firm effects (the identifiable effects). The computati ..."
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Cited by 141 (16 self)
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other employer in the group. This algorithm finds all of the maximally connected subgraphs of a graph. The relevant graph has a set of vertices that is the union of the set of persons and the set of firms and edges that are pairs of persons and firms. An edge (i,j) is in the graph if person i has
A note on the connectivity of the Cartesian product of graphs
"... We present an example of two connected graphs for which the connectivity of the Cartesian product of the graphs is strictly greater than the sum of the connectivities of the factor graphs. This clarifies an issue from the literature. We then find necessary and sufficient conditions for the connectiv ..."
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for the connectivity of the Cartesian product of the graphs to be equal to the sum of the connectivities of the individual graphs. Throughout this paper we strive to use general terminology in graph theory from [3], and terminology concerning Cartesian products of graphs from [4]. Let G =(V (G),E(G)) be a graph
The formalization of simple graphs
 Journal of Formalized Mathematics
, 1994
"... Summary. A graph is simple when • it is nondirected, • there is at most one edge between two vertices, • there is no loop of length one. A formalization of simple graphs is given from scratch. There is already an article [10], dealing with the similar subject. It is not used as a startingpoint, be ..."
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Cited by 21 (0 self)
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, • equality relation on graphs. • the notion of degrees of vertices; the number of edges connected to, or the number of adjacent vertices, • the notion of subgraphs, • path, cycle, • complete and bipartite complete graphs, Theorems proved in this articles include: • the set of simple graphs satisfies a
Results 1  10
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128