摘要:
正 文獻(xiàn)[1]曾用有向圖表示一組線性方程,然后利用這個(gè)圖(稱為流圖或Coates圖)寫出方程的解。此法在各方面,尤其是在電路理論方面得到廣泛的應(yīng)用,不過在計(jì)算中需要列舉流圖中全部1-因子(1-factor)和1-因子連通(1-factorial connection),對于較復(fù)雜
Abstract:
This note gives a method to find all the 1-factors and 1-factorial connections of a flow graph. Let (D) be the set of all subgraphs of a given diagraph G(V, E) and (H) be the set of all subsets of (D). For h1, h2 (H), a multiplication operation being called star is denoted by the symbol * and is defined in the following: h1,*h2 ={xy/xh1, yh2, and deg+xy(i)2, deg-xy(i)2}. Theorem Let G(V, E) be a diagraph with vertex set V={1, 2,,}, and let Sk={(k, t)/(k, t) E, t V}. Then all the 1-factors of G(V,E) can be determined by the product of Sk as follows:C=S1*S2**S Obviously, if G(V,E) is replaced by G(V, E) is replaced by G(V, E)U(j, i), (j, i) E, then the product gives all the 1-factorial connections from em to j of the diagraph G(V, E).
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