关于DNA图及其标号图的进一步研究

The Further Study on DNA Graphs and DNA Labeling Graphs

2007年,Wang等得到了关于不包含环的DNA标号图的一个结果,在此基础上我们推广到一般有向图上,即任何无孤立点的有向图在友关系下恰有—个等价类的充要条件,并得出几个相应的改进结果.本文还给出了一个定理的反例,进而得到定理的修正和完善.由此容易推出Wang等的一个定理的必要条件也是充分的.

In 2007,Wang obtained a result about DNA labeling graphs which do not contain loops.On this basis,we generalized a sufficient and necessary condition for general directed graphs.We conclude that the sufficient and necessary condition for any directed graphs,which do not contain isolated vertices have and only have a equivalence class under the friend relationship and we draw some improved results accordingly.A counterexample of a theorem is given,too.Furthermore,we modified and completed this theorem.It is easy to deduce that the necessary condition for the theorem in Wang＇s research is also a sufficient condition.