The symmetry property of (n,k)‐arrangement graph

2021 ◽  
Author(s):  
Fu‐Gang Yin ◽  
Yan‐Quan Feng ◽  
Jin‐Xin Zhou ◽  
Yu‐Hong Guo
Keyword(s):  
Symmetry Property ◽  
Arrangement Graph

On the Radial Symmetry Property for Harmonic Functions

2020 ◽  
Vol 64 (10) ◽  
pp. 9-19
Author(s):  
V. V. Volchkov ◽  
Vit. V. Volchkov
Keyword(s):  
Harmonic Functions ◽  
Symmetry Property ◽  
Radial Symmetry

On the arrangement graph

1998 ◽  
Vol 66 (4) ◽  
pp. 215-219 ◽  
Author(s):  
Wei-Kuo Chiang ◽  
Rong-Jaye Chen
Keyword(s):  
Arrangement Graph

Adsorption‐stretching analogy for a polymer chain on a plane. Symmetry property of the phase diagram

1994 ◽  
Vol 100 (3) ◽  
pp. 2325-2334 ◽  
Author(s):  
Aleksandr M. Skvortsov ◽  
Aleksey A. Gorbunov ◽  
Leonid I. Klushin
Keyword(s):  
Phase Diagram ◽  
Polymer Chain ◽  
Symmetry Property ◽  
Plane Symmetry

A Note of Independent Number and Domination Number of Qn,k,m-Graph

2019 ◽  
Vol 29 (03) ◽  
pp. 1950011
Author(s):  
Jiafei Liu ◽  
Shuming Zhou ◽  
Zhendong Gu ◽  
Yihong Wang ◽  
Qianru Zhou
Keyword(s):  
Interconnection Networks ◽  
Interconnection Network ◽  
Domination Number ◽  
Multiprocessor System ◽  
Star Graph ◽  
Minimum Cardinality ◽  
Arrangement Graph ◽  
Independent Number ◽  
Potential Applications ◽  
By Products

The independent number and domination number are two essential parameters to assess the resilience of the interconnection network of multiprocessor systems which is usually modeled by a graph. The independent number, denoted by [Formula: see text], of a graph [Formula: see text] is the maximum cardinality of any subset [Formula: see text] such that no two elements in [Formula: see text] are adjacent in [Formula: see text]. The domination number, denoted by [Formula: see text], of a graph [Formula: see text] is the minimum cardinality of any subset [Formula: see text] such that every vertex in [Formula: see text] is either in [Formula: see text] or adjacent to an element of [Formula: see text]. But so far, determining the independent number and domination number of a graph is still an NPC problem. Therefore, it is of utmost importance to determine the number of independent and domination number of some special networks with potential applications in multiprocessor system. In this paper, we firstly resolve the exact values of independent number and upper and lower bound of domination number of the [Formula: see text]-graph, a common generalization of various popular interconnection networks. Besides, as by-products, we derive the independent number and domination number of [Formula: see text]-star graph [Formula: see text], [Formula: see text]-arrangement graph [Formula: see text], as well as three special graphs.

A global random walk on spheres algorithm for transient heat equation and some extensions

2019 ◽  
Vol 25 (1) ◽  
pp. 85-96 ◽  
Author(s):  
Karl K. Sabelfeld
Keyword(s):  
Random Walk ◽  
Heat Equation ◽  
Symmetry Property ◽  
Forthcoming Paper ◽  
Diffusion Reaction ◽  
Advection Diffusion ◽  
The Green Function ◽  
Walk On Spheres Algorithm ◽  
Reaction Equations ◽  
Advection Diffusion Reaction Equations

AbstractWe suggest in this paper a global Random Walk on Spheres (gRWS) method for solving transient boundary value problems, which, in contrast to the classical RWS method, calculates the solution in any desired family ofmprescribed points. The method uses onlyNtrajectories in contrast tomNtrajectories in the conventional RWS algorithm. The idea is based on the symmetry property of the Green function and a double randomization approach. We present the gRWS method for the heat equation with arbitrary initial and boundary conditions, and the Laplace equation. Detailed description is given for 3D problems; the 2D problems can be treated analogously. Further extensions to advection-diffusion-reaction equations will be presented in a forthcoming paper.

Symmetry property of a generalized Billet's N-split lens

2010 ◽  
Vol 283 (19) ◽  
pp. 3564-3568 ◽  
Author(s):  
Chieh-Jen Cheng ◽  
Jyh-Long Chern
Keyword(s):  
Symmetry Property
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