On the shannon capacity of a graph
Web24 de out. de 2024 · The Shannon capacity models the amount of information that can be transmitted across a noisy communication channel in which certain signal values … WebA well-characterized, and in a sense easily computable, function is introduced which bounds the capacity from above and equals the capacity in a large number of cases. Several results are obtained on the capacity of special graphs; for example, the Petersen graph has capacity four and a self-complementary graph with n points and with a vertex …
On the shannon capacity of a graph
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Web1 de mar. de 2024 · Our bounds strengthen the Kneser conjecture, proved by Lovász in 1978, and some of its extensions due to Bárány, Schrijver, Dol’nikov, and Kriz. As applications, we determine the integrality gap of fractional upper bounds on the Shannon capacity of graphs and the quantum one-round communication complexity of certain … WebIn graph theory, the Lovász number of a graph is a real number that is an upper bound on the Shannon capacity of the graph. It is also known as Lovász theta function and is commonly denoted by (), using a script form of the Greek letter theta to contrast with the upright theta used for Shannon capacity. This quantity was first introduced by László …
Web25 de jul. de 2016 · We derive upper and lower bounds on the $\rho$-capacity of arbitrary graphs, and provide a Lovász-type upper bound for regular graphs. We study the behavior of the $\rho$-capacity under two graph operations: the strong product and the disjoint union. Finally, we investigate the connection between the structure of a graph and its … WebThe Shannon capacity of a graph and the independence numbers of its powers. It is shown that the series of independence numbers in strong powers of a fixed graph can …
In graph theory, the Shannon capacity of a graph is a graph invariant defined from the number of independent sets of strong graph products. It is named after American mathematician Claude Shannon. It measures the Shannon capacity of a communications channel defined from the graph, and is upper bounded by the Lovász number, which can be computed in polynomial time. However, the computational complexity of the Shannon capacity itself remains unknown. Web14 de abr. de 2024 · In the estuary and nearshore environments, suspended particulate matter (SPM) plays a particularly important role. This article presents a study on the suspended particulate matter and microbial communities in the euphotic zone of China’s nearshore and estuarine regions. The study used various analytical techniques, including …
Web25 de jul. de 2016 · Motivated by the problem of zero-error broadcasting, we introduce a new notion of graph capacity, termed -capacity, that generalizes the Shannon …
WebHá 1 dia · This study was conducted on soil polluted with high concentrations of crude oil (12835±572.76 mg/kg) with different dosages of persulfate (PS) coupled with hydrocarbon-degrading mixed bacteria (including Enterobacteriaceae, Stenotrophomonas, Pseudomonas, Acinetobacter, and Achromobacter) obtained from long-term oil-contaminated soil.. The … sharp pains in right chestWeb24 de abr. de 2006 · Abstract: The independence numbers of powers of graphs have been long studied, under several definitions of graph products, and in particular, under the … porphyry nodes mtgWebThe Shannon capacity is in general very difficult to calculate (Brimkov et al. 2000).In fact, the Shannon capacity of the cycle graph was not determined as until 1979 (Lovász … porphyry mineralization in the tethyan orogenWebAbstract: We present randomized approximation algorithms for the maximum cut (MAX CUT) and maximum 2-satisfiability (MAX 2SAT) problems that always deliver solutions of expected value at least.87856 times the optimal value. These algorithms use a simple and elegant technique that randomly rounds the solution to a nonlinear programming … sharp pains in pelvic areaWeb1 de dez. de 1985 · The Shannon capacity problem in undirected graphs is well known [7]. This problem can be naturally generalized in the case of directed graphs and we find, in … porphyry imageWeb18 de ago. de 2013 · Graph theorists have many measures of how ‘big’ a graph is: order, size, diameter, radius, circumference, girth, chromatic number, and so on. Last time I told you about two of them: independence number and Shannon capacity.This time I’ll bring in two other measures of size that I’ve written about previously in contexts other than graph … sharp pains in my right temple areaWeb24 de dez. de 2012 · Using the above argument, Leung et al. recently found the first two examples of graphs whose entanglement-assisted capacity exceeds the Shannon capacity.Their graphs are based on the exceptional root systems and , giving a graph on 63 vertices such that and a graph on 157 vertices such that .They also show that their … sharp pains in thigh