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  • 1972
  • Issue No. 6 - June
  • 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
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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