@article {
author = {Abdollahi, Alireza},
title = {Determinants of adjacency matrices of graphs},
journal = {Transactions on Combinatorics},
volume = {1},
number = {4},
pages = {9-16},
year = {2012},
publisher = {University of Isfahan},
issn = {2251-8657},
eissn = {2251-8665},
doi = {10.22108/toc.2012.2041},
abstract = {We study the set of all determinants of adjacency matrices of graphs with a given number of vertices. Using Brendan McKay's data base of small graphs, determinants of graphs with at most $9$ vertices are computed so that the number of non-isomorphic graphs with given vertices whose determinants are all equal to a number is exhibited in a table. Using an idea of M. Newman, it is proved that if $G$ is a graph with $n$ vertices, $m$ edges and $\{d_1,\dots,d_n\}$ is the set of vertex degrees of $G$, then $\gcd(2m,d^2)$ divides the determinant of the adjacency matrix of $G$, where $d=\gcd(d_1,\dots,d_n)$. Possible determinants of adjacency matrices of graphs with exactly two cycles are obtained.},
keywords = {Determinant,adjacency matrices of graphs,maximum determinant},
url = {https://toc.ui.ac.ir/article_2041.html},
eprint = {https://toc.ui.ac.ir/article_2041_b9579dd3348af7ab9be7b60997202498.pdf}
}