- 
							
								Lei Wang
							
              						
 
											- 
							
								Cai Heng Li
							
              						
 
											- 
							
								Yin Liu
							
              						
 
											- 
							
								Ci Xuan Wu
							
              						
 
									
			
																												
							
									
				
										Keywords:
				
				
																		Self-complementary graph, 													Cayley graph, 													Fixed-point-free automorphism															
			
			
										
					
Abstract
					Self-complementary Cayley graphs are useful in the study of Ramsey numbers, but they are relatively very rare and hard to construct. In this paper, we construct several families of new self-complementary Cayley graphs of order $p^4$ where $p$ is a prime and congruent to $1$ modulo $8$.