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In this paper, subgraphs and complementary graphs are used to analyze the network synchronizability. Some sharp and attainable bounds are provided for the eigenratio of the network structural matrix, which characterizes the network synchronizability, especially when the networks corresponding graph has cycles, chains, bipartite graphs or product graphs as its subgraphs.
In this paper, we consider a variant of Ramsey numbers which we call complementary Ramsey numbers $bar{R}(m,t,s)$. We first establish their connections to pairs of Ramsey $(s,t)$-graphs. Using the classification of Ramsey $(s,t)$-graphs for small $s,
It is an intriguing question to see what kind of information on the structure of an oriented graph $D$ one can obtain if $D$ does not contain a fixed oriented graph $H$ as a subgraph. The related question in the unoriented case has been an active are
We assess electrical brain dynamics before, during, and after one-hundred human epileptic seizures with different anatomical onset locations by statistical and spectral properties of functionally defined networks. We observe a concave-like temporal e
Kuhn, Osthus and Taraz showed that for each gamma>0 there exists C such that any n-vertex graph with minimum degree gamma n contains a planar subgraph with at least 2n-C edges. We find the optimum value of C for all gamma<1/2 and sufficiently large n.
Measuring network flow sizes is important for tasks like accounting/billing, network forensics and security. Per-flow accounting is considered hard because it requires that many counters be updated at a very high speed; however, the large fast memori