9,621 research outputs found
The domination number and the least -eigenvalue
A vertex set of a graph is said to be a dominating set if every
vertex of is adjacent to at least a vertex in , and the
domination number (, for short) is the minimum cardinality
of all dominating sets of . For a graph, the least -eigenvalue is the
least eigenvalue of its signless Laplacian matrix. In this paper, for a
nonbipartite graph with both order and domination number , we show
that , and show that it contains a unicyclic spanning subgraph
with the same domination number . By investigating the relation between
the domination number and the least -eigenvalue of a graph, we minimize the
least -eigenvalue among all the nonbipartite graphs with given domination
number.Comment: 13 pages, 3 figure
Stochastic Averaging Principle for Dynamical Systems with Fractional Brownian Motion
Stochastic averaging for a class of stochastic differential equations (SDEs)
with fractional Brownian motion, of the Hurst parameter H in the interval (1/2,
1), is investigated. An averaged SDE for the original SDE is proposed, and
their solutions are quantitatively compared. It is shown that the solution of
the averaged SDE converges to that of the original SDE in the sense of mean
square and also in probability. It is further demonstrated that a similar
averaging principle holds for SDEs under stochastic integral of pathwise
backward and forward types. Two examples are presented and numerical
simulations are carried out to illustrate the averaging principle
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