Graphs with prescribed connectivities

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August undefined, 2024

WebA graph G is locally n-connected (locally n-edge connected) if the neighborhood of each vertex of G is n-connected (n-edge connected). The local connectivity (local edge-connectivity) of G is the maximum n for which G is locally n-connected (locally n-... WebRendiconti del Circolo Matematico di Palermo Series 2 - G. Chartrand and F. Harary,Graphs with prescribed connectivities, 1966, Symp. on Graph Theory, Tihany, Acad ...

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WebAug 20, 2001 · Request PDF Edge Connectivity vs Vertex Connectivity in Chordal Graphs It is well known that in a graph, κ(G)≤λ(G) ≤ δ(G), where κ (G), δ(G) and d(G) denote the vertex connectivity ... WebOct 11, 2024 · Generalizing well-known results of Erdős and Lovász, we show that every graph G contains a spanning k-partite subgraph H with λ (H) ≥ k − 1 k λ (G), where λ (G) is the edge-connectivity of G.In particular, together with a well-known result due to Nash-Williams and Tutte, this implies that every 7-edge-connected graph contains a spanning … something that interferes

Lower bounds on the vertex-connectivity of digraphs and graphs

WebThe theory of connectivity is extended from graphs to digraphs by introducing connectivity measures similar to the well-known point- and line-connectivities for graphs. Some … WebOct 25, 2011 · We present a new algebraic formulation to compute edge connectivities in a directed graph, using the ideas developed in network coding. This reduces the problem of computing edge connectivities to solving systems of linear equations, thus allowing us to use tools in linear algebra to design new algorithms. Using the algebraic formulation we … WebAbstract. A graph G is locally n-connected (locally n-edge connected) if the neighborhood of each vertex of G is n-connected (n-edge connected). The local connectivity (local edge … something that is 20 feet long

The minimum degree and connectivity of a graph

On local connectivity of graphs - ScienceDirect

WebJan 1, 2006 · These subgraph connectivity numbers are shown to be ordered by ω-1 $\leqslant \hat \kappa \leqslant \hat \lambda \leqslant \hat \delta$ for any graph. … something that holds things togetherWebChartrand and Harary [Graphs with prescribed connectivities, in: P. Erdös, G. Katona (Eds.), Theory of Graphs, Aca... Let G be a graph of order n( G), minimum degree ý( G) … something that interests you

"Webgraph to be 2-connected. In [1 i]t was shown tha it f every point of a graph G with p points has degree not less than (p + n — 2)/2, then G is n-connected. Posa's theorem th suggeste follow-s ing improvement. THEOREM. Let G be a graph with p(^ 2) points and let 1 ^ n < p. The follow-ing conditions are sufficient for G to be n-connected: " - Graphs with prescribed connectivities

Graphs with prescribed connectivities

Lower bounds on the vertex-connectivity of digraphs and graphs

WebFeb 26, 2010 · A graph G (finite, undirected, and without loops or multiple lines) is n-connected if the removal of fewer than n points from G neither disconnects it nor reduces … Webconnectivities from s to all vertices can be computed in O(nω/2)time. For general directed graphs, we show that all pairs edge connectivities can be computed in one matrix inverse time, instead of solving linear equations for each source vertex separately. The algorithm is faster when m=O(n1.93),for example when m = O(n) it takes O(nω) time ...

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WebAug 12, 2024 · Abstract: Generalizing well-known results of Erdős and Lovász, we show that every graph $G$ contains a spanning $k$-partite subgraph $H$ with … WebSep 1, 2024 · Request PDF On Sep 1, 2024, B.A. Terebin and others published On the optimality of graph implementations with prescribed connectivities Find, read and cite all the research you need on ...

WebOct 3, 2006 · This article presents a study of the connectivities of a graph as a function of other graph parameters such as the number of vertices, the maximum degree, and the … WebChartrand and Harary [Graphs with prescribed connectivities, in: P. Erdös, G. Katona (Eds.), Theory of Graphs, Aca... Let G be a graph of order n( G), minimum degree ý( G) and connectivity ý( G). On the connectivity of diamond-free graphs …

WebABSTRACT In this paper we extend the theory of connectivity from graphs to digraphs by introducing connectivity measures similar to the wellknown point- and line-connectivities for graphs. We discuss some simple upper and lower bounds for these parameters, and present classes of digraphs with various prescribed connectivities. Web2. A k-edges connected graph is disconnected by removing k edges Note that if g is a connected graph we call separation edge of g an edge whose removal disconnects g …

WebJan 1, 2006 · G. Chartrand, A graph-theoretic approach to a communications problem. J. SIAM Appl. Math. 14 (1966) 778–781. CrossRef MathSciNet MATH Google Scholar G. Chartrand and F. Harary, Graphs with prescribed connectivities. Theory of Graphs (P. Erdös and G. Katona, Eds.) Akadémiai Kiadó, Budapest, 1968, 61–63.

WebJan 7, 2010 · G. Gentile, in Encyclopedia of Mathematical Physics, 2006 Graphs and Trees. A (connected) graph G is a collection of points, called vertices, and lines connecting all … something that i can drawWebJul 31, 2006 · Since interconnection networks are often modeled by graphs or digraphs, the connectivity of a (di-)graph is an important measurement for fault tolerance of networks.Let G be a graph of order n, minimum degree δ, and vertex-connectivity k. If G is not ... something that invalidateshttp://www-scf.usc.edu/~hoyeeche/papers/connectivity_conf.pdf something that is 6 inchesWebAug 23, 2024 · Let 'G' be a connected graph. The minimum number of vertices whose removal makes 'G' either disconnected or reduces 'G' in to a trivial graph is called its … something that helps you fall asleepWebscanpy.tl.paga scanpy.tl. paga (adata, groups = None, use_rna_velocity = False, model = 'v1.2', neighbors_key = None, copy = False) Mapping out the coarse-grained connectivity structures of complex manifolds [Wolf19].. By quantifying the connectivity of partitions (groups, clusters) of the single-cell graph, partition-based graph abstraction (PAGA) … something that i canWebTen major topics ? profusely illustrated ? include: Mathematical Models, Elementary Concepts of Graph Theory, Transportation Problems, Connection Problems, Party … something that is 6 feetWebSep 1, 2024 · Request PDF On Sep 1, 2024, B.A. Terebin and others published On the optimality of graph implementations with prescribed connectivities Find, read and … something that is 63 ii inches long