4,184 research outputs found
On Domination Number and Distance in Graphs
A vertex set of a graph is a \emph{dominating set} if each vertex of
either belongs to or is adjacent to a vertex in . The
\emph{domination number} of is the minimum cardinality of
as varies over all dominating sets of . It is known that , where denotes the diameter of . Define
as the largest constant such that for any vertices of an arbitrary connected graph ;
then in this view. The main result of this paper is that
for . It immediately follows that
, where and are
respectively the average distance and the Wiener index of of order . As
an application of our main result, we prove a conjecture of DeLaVi\~{n}a et
al.\;that , where denotes the
eccentricity of the boundary of an arbitrary connected graph .Comment: 5 pages, 2 figure
Domination in Functigraphs
Let and be disjoint copies of a graph , and let be a function. Then a \emph{functigraph}
has the vertex set and the edge set . A functigraph is a
generalization of a \emph{permutation graph} (also known as a \emph{generalized
prism}) in the sense of Chartrand and Harary. In this paper, we study
domination in functigraphs. Let denote the domination number of
. It is readily seen that . We
investigate for graphs generally, and for cycles in great detail, the functions
which achieve the upper and lower bounds, as well as the realization of the
intermediate values.Comment: 18 pages, 8 figure
Improving the Accuracy of the Diffusion Model in Highly Absorbing Media
The diffusion approximation of the Boltzmann transport equation is
most commonly used for describing the photon propagation in turbid
media. It produces satisfactory results in weakly absorbing and highly
scattering media, but the accuracy lessens with the decreasing albedo.
In this paper, we presented a method to improve the accuracy of the
diffusion model in strongly absorbing media by adjusting the optical parameters. Genetic algorithm-based optimization tool is used to find the
optimal optical parameters. The diffusion model behaves more closely to
the physical model with the actual optical parameters substituted by the
optimized optical parameters. The effectiveness of the proposed technique
was demonstrated by the numerical experiments using the Monte Carlo
simulation data as measurements
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