vol18_pp162-175. 161KB Jun 04 2011 12:06:02 AM
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![Figure A2] to construct a potentially stable sign pattern of order 5 with these r-cycles.](https://thumb-ap.123doks.com/thumbv2/123dok/959810.911138/11.612.74.422.205.370/figure-construct-potentially-stable-sign-pattern-order-cycles.webp)
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Schur complement, LU factorization, Bipartite graph, Sign pattern, Zero pattern, Nearly reducible matrix, Minimally strongly connected digraph.. AMS
To under- stand why the corresponding statement of Theorem 1.1 could fail for directed graphs we connect the Laplacian for a directed graph with the Laplacian for a
Moreover, the minimum (resp. maximum) number of edges for all (connected) graphs with pendent vertices and nullity η are determined, and the extremal graphs are characterized..
In this paper, by investigating the Perron vector of G, we show that type-I-a graphs are not λ 1 -extremal graphs, and type-I-b (resp. type-II-a) graphs with some.. specified
If a pattern A allows every possible refined inertia, then A is a refined inertially arbitrary pattern (rIAP), and this notion is defined analogously for sign patterns.. The reversal
These results are used to characterize all extremal weighted trees with the largest p -Laplacian spectral radius among all weighted trees with a given degree sequence and a
For a zero-delayed random walk on the real line, let τ (x), N(x) and ρ (x) denote the first passage time into the interval (x, ∞ ), the number of visits to the interval ( −∞ , x]
It is straightforward to check that the set of eventually active sites in the local bootstrap percolation model is identical to the limiting rectangle lim i →∞ ρ i , and in
