Pulsar death line can be defined in a P-P diagram. Traditionally, radio-loud pulsars are supposed to locate above the death line where there is a radio-loud region. With the development of observational equipment, the observational properties of the neutron star are remarkably diverse. In a P-P diagram, some of the special sources are radio-quiet but lie above the death line. From the definition of the pulsar death line, different equations of state for a neutron star or strange star result in different death lines. We discuss the influence of the equation of state on the pulsar death line and the possible link between different neutron star groups. The results show that central compact objects would be the small mass of self-bound strange stars, and rotating radio transients might be old pulsars on the verge of death. We suggest that PSR J2144-3933 is likely to be a large mass pulsar, which would be larger than 2.0 M-circle dot. Multiple observational facts would help us to reveal the nature of pulsars.