CAJ | 학술논문

图的零度是指在图的谱中特征值0的重数.在文献[2]中作者给出了刻画非奇异单圈图的充分条件,并提出了一个问题,即这个条件是否也是必要的.在本文中,我们先对这个问题作出肯定回答,然后介绍一个新的概念:保留点,最后通过最大匹配数给出公式计算单圈图的零度.
도적령도시지재도적보중특정치0적중수.재문헌[2]중작자급출료각화비기이단권도적충분조건,병제출료일개문제,즉저개조건시부야시필요적.재본문중,아문선대저개문제작출긍정회답,연후개소일개신적개념:보류점,최후통과최대필배수급출공식계산단권도적령도.
The nullity of a graph is the multiplicity of the eigenvalue zero in its spectrum. Recently, Tan Xuezhong and Liu Bolian in [2] obtained a sufficient condition for the unicyclic graphs with nullity 0 and asked a problem that if this condition is also necessary. In this paper, we first give the confirm answer for this problem. Next we introduce a new notion of PED-graph and give a formula to calculate its nullity by means of maximum matching number and then the nullity of unicyclic graph is completely determined.