ConnectivityAdjacency eigenvalueLaplacian eigenvalueSignless Laplacian eigenvalueQuotient matrixLet κ(G), g(G), δ(G) and Δ(G) denote the vertex-connectivity, the girth, the minimum degree and the maximum degree of a simple graph G, and let λi(G), μi(G) and qi(G) denote the ith...
Reconstruct the metric graph taking into account that the vertex conditions respect connectivity of the graph. Write the vertex conditions using the other two standard parametrisations: (1) via the vertex scattering matrix (canonical); (2) via subspaces and Hermitian matrices (Kuchment). Hint: ...
On the connectivity of Cartesian product of graphs We give a new alternative proof of Liouville's formula which states that for any graphs G and H on at least two vertices, κ ( G □ H )=min{ κ ... J Govorčin,R Škrekovski - 《Ars Mathematica Contemporanea》 被引量: 46发表...
A typical problem in network design is to find a minimum-cost sub-network H of a given network G such that H satisfies some prespecified connectivity requi... J Cheriyan,S Vempala,A Vetta - 《Combinatorica》 被引量: 109发表: 2006年 SUBSET ALGEBRA LIFT OPERATORS FOR 0-1 INTEGER PROGRAMM...
As a solution researchers began to providespace-efficientalgorithms and data structures to solve basic problems like graph-connectivity problems [3,5,14,20,24], other graph problems [27,32], memory initialization [26,33], dictionaries with constant-time operations [12,15,23] or graph interfaces...
Minimal vertex covers on finite-connectivity random graphs: A hard-sphere lattice-gas picture The minimal vertex-cover (or maximal independent-set) problem is studied on random graphs of finite connectivity. Analytical results are obtained by a mapp... Martin,Weigt,Alexander,... - 《Physical Revi...
Vertex of a Parabola Main Concept The vertex of a parabola is the point at the intersection of the parabola and its line of symmetry. For a parabola whose equation is given in standard form , the vertex will be the minimum (lowest point) of the graph...
connectivity [15]. Hierarchical clustering methods based on global metric over nodes or edges, such as betweenness centralities, are very time-consuming, and thus do not scale well to large PINs. The few hierarchical approaches based on local metric also have the common problem of classifying ...
In the Directed Feedback Vertex Set (DFVS) problem, the input is a directed graph D and an integer k. The objective is to determine whether there exists a
To bound the first summand on the right hand side, we apply the many-to-one formula (Proposition 2.15) with \eta = 1, and get a random walk (S_{i})_{i\ge 0}, such that \begin{aligned} \begin{aligned}&\hspace{-8em} \mathbb {P}[\exists |x|=n,\text { such that } \for...