Power graphs via their characteristic polynomial

Document Type : Original Article


Department of Mathematics, Faculty of Science, Shahid Rajaee Teacher Training University, Tehran, 16785-163, I. R. Iran


A power graph is defined a graph that it's vertices are the elements of group and two vertices are adjacent if and only if one of them is a power of the other. Suppose $A(X)$ is the adjacency matrix of graph $X$. Then the polynomial $\chi(X,\lambda)=det(xI-A(X))$ is called as characteristic polynomial of $X$. In this paper,  we compute the characteristic polynomial of all power graphs of order $p^2q$, where $p,q$ are distinct prime numbers.


Volume 8, Issue 3
September 2023
Pages 187-199
  • Receive Date: 02 July 2023
  • Revise Date: 22 July 2023
  • Accept Date: 29 August 2023
  • Publish Date: 01 September 2023