Central Tehran Branch, Islamic Azad UniversityJournal of Linear and Topological Algebra (JLTA)2252-0201080120190201Albertson energy and Albertson Estrada index of graphs1124546046ENA. JahanbaniDepartment of Mathematics, Shahrood University of Technology, Shahrood, IranJournal Article20180707Let $G$ be a graph of order $n$ with vertices labeled as $v_1, v_2,dots , v_n$. Let $d_i$ be the degree of the vertex $v_i$ for $i = 1, 2, cdots , n$. The Albertson matrix of $G$ is the square matrix of order $n$ whose $(i, j)$-entry is equal to $|d_i - d_j|$ if $v_i $ is adjacent to $v_j$ and zero, otherwise. The main purposes of this paper is to introduce the Albertson energy and Albertson-Estrada index of a graph, both base on the eigenvalues of the Albertson matrix. Moreover, we establish upper and lower bounds for these new graph invariants and relations between them.http://jlta.iauctb.ac.ir/article_546046_a9e9d6f8e6b5ede19ce15c13c7ad337c.pdf