拓展圖的一般理論
A UNIFIED THEORY OF AUGMENTED GRAPH
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摘要: 本文提出拓展圖的統(tǒng)一理論。文中證明了兩個(gè)矩陣運(yùn)算的數(shù)學(xué)定理。以此為基礎(chǔ),給出矩陣行列式、代數(shù)余子式和線性方程組的拓展圖計(jì)算法,并就拓展科茨(Coales)和拓展梅森(Mason)圖進(jìn)行了拓?fù)浜?jiǎn)化。拓展圖理論的建立使現(xiàn)行網(wǎng)絡(luò)拓?fù)淅碚摰慕Y(jié)構(gòu)大為縮減。
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關(guān)鍵詞:
Abstract: This paper presents a unified theory of augmented graph. Two basic theorems for a matrix are proved. By making use of graph augmentation, evaluation of the determinant and cofactors associated with a matrix is carried out in one single analysis which is referred to the J-operation, so that is of a set of linear algebraic equations. The augmented Coates graph and Mason graph are topologically simplified. Since the need for the formulas called D-operation is eliminated, the augmented graph serves as a theoretic basis, on which the existing network topology could be reduced greatly. -
P. M. Lin, IEEE Trans. on CT, CT-20(1973), 732.[2]G. E. Alderson et. al.,ibid., CT-20(1973), 48.[3]胡宗煊等,山東大學(xué)學(xué)報(bào)(自然科學(xué)版),1984年第1期第35頁.[4]胡宗煊等,電子科學(xué)學(xué)刊,6(1985), 180.[5]Ф.Р.Гантмахер著,柯召譯,矩陣論(上卷),高等教育出版社,1955,第2章.[6]W. K. Chen, Applied Graph Theory, Amsterdam: North-Holland, 1976, Chs. 3-4.[7]Z. X. Hu(胡宗煊), Directed tree Solutions to Linear Network Systems Proc. of Int. Conf. on Computers, Systems and Signal Processing, Bangalore, India, 1984. -
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