加权T-图活性的进一步研究

FURTHER RESEARCH OF LIVENESS FOR WEIGHTED T-GRAPHS

本文给出加权T-图是活网的另一组充分条件，这组条件包含了Teruel等对加权T-图活性分析的结果，方法简单，便于操作．Teruel文中研究了加权单回路网为守恒回路时活的一个充分条件，对一般加权T-图活性的判断只限于每个回路是守恒回路的情况．许安国等1993年给出判断加权T-图是活网的充分必要条件，但方法繁琐，操作不方便．本文克服了原文的缺点，保留了Teruel文的优点，同时又扩大了Teruel文中定理4．12的使用范围，对于每个回路可以是守恒回路或增加回路．

This paper presents a set of sufficient conditions for the liveness ofweighted T-graphs, this set of conditions involves the condition given in Teruel'spapers for the liveness of weighted T-graphs, the given technique is simple andeasy to operate. In Teruel's paper, a sufficient condition has been studied for theliveness of weighted circuit net which is conservative circuit, the decision for theliveness of comrnon weighted T-graphs is only feasible in the case that every circuitis conservative one. Xu et al. proposed a necessary and sufficient condition in 1993to decide the liveness of weighted TAigraphs, but it is too complex to operate. Thispaper surmounts the shortcorning of Xu's paper, preserves the superiority ofTeruel's paper, and further more enlarges the adaptable range of theorem 4. 12 inTeruel's paper, that means in this paper, whether circuit in weighted T-graphs isconservative or gain circuit, the theorem always works.