پديدآورندگان :
Aaghabali M mehdi.aaghabali@ed.ac.uk, School of Mathematics, The University of Edinburgh, James Clerk Maxwell Building, The Kings Buildings, Mayfield Road EH9 3JZ, Edinburgh , Akbari S s_akbari@sharif.edu Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran , Csikvari P peter.csikvari@gmail.com Eötvös Loránd University, Budapest, Hungary , Tajfirouz Z z_tajfirouz@yahoo.com School of Mathematics, The University of Edinburgh, James Clerk Maxwell Building, The Kings Buildings, Mayfield Road EH9 3JZ, Edinburgh
چكيده فارسي :
Let G be a graph with the vertex set V (G) and edge set E(G) and the adjacency matrix A. The permanental polynomial of G is defined as π(G,x) = per(xI − A). The roots of permanental polynomial are called permanental roots of G. In this paper we study graphs whose absolute values of their permanental roots do not exceed 1 and show that every connected graph except P2 has some permanental roots out of unit cycle. Also, we characterize graphswithafewdistinctpermanentalroots. Inthispaperweprovethatonly connected graph with exactly two distinct permanental roots are the path of order 2 and cycle of order 4.
