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  • Abstract - Contradiction Equations in a B Matrix of Vertex Weight Method and Their Correspondence with the k-Summability Property of Vertices
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Contradiction Equations in a B Matrix of Vertex Weight Method and Their Correspondence with the k-Summability Property of Vertices
June 1972 (vol. 21 no. 6)
pp. 606-610
ASCII Text
x 
 
H. R. Hwa, "Contradiction Equations in a B Matrix of Vertex Weight Method and Their Correspondence with the k-Summability Property of Vertices," IEEE Transactions on Computers, vol. 21, no. 6, pp. 606-610, June, 1972.
 
 
BibTex
x
 
@article{ 10.1109/TC.1972.5009019,
author = {H. R. Hwa},
title = {Contradiction Equations in a B Matrix of Vertex Weight Method and Their Correspondence with the k-Summability Property of Vertices},
journal ={IEEE Transactions on Computers},
volume = {21},
number = {6},
issn = {0018-9340},
year = {1972},
pages = {606-610},
doi = {http://doi.ieeecomputersociety.org/10.1109/TC.1972.5009019},
publisher = {IEEE Computer Society},
address = {Los Alamitos, CA, USA},
}
 
 
RefWorks Procite/RefMan/Endnote
x 
 
TY - JOUR
JO - IEEE Transactions on Computers
TI - Contradiction Equations in a B Matrix of Vertex Weight Method and Their Correspondence with the k-Summability Property of Vertices
IS - 6
SN - 0018-9340
SP606
EP610
EPD - 606-610
A1 - H. R. Hwa,
PY - 1972
VL - 21
JA - IEEE Transactions on Computers
ER -
 
H. R. Hwa, Basser Computing Department, University of Sydney, Sydney, New South Wales, Australia.
This note attempts to show that, in a vertex weight method [1], every contradiction equation bears a one-to-one correspondence with the summability pair C1S, C2S, where C1S = {X11, X12, ..., X1k}¿ C1 C2S = {X21, X22,..., X2k} ¿ C2 and vector sums of the vertices plz check [Eqa] The vertices, Xki's, K = 1, or 2, are not necessarily distinct, and C1, C2 are two disjoint sets of vertices in En space. As a consequence, the contradiction equation is a necessary and sufficient condition that the homogeneous system, solved for a threshold function of order r, has no solution. This tells that the threshold function is of order greater than r.
Citation:
H. R. Hwa, "Contradiction Equations in a B Matrix of Vertex Weight Method and Their Correspondence with the k-Summability Property of Vertices," IEEE Transactions on Computers, vol. 21, no. 6, pp. 606-610, June 1972, doi:10.1109/TC.1972.5009019
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