Albertson energy and Albertson Estrada index of graphs
Subject Areas : Algebraic topology
A.
Jahanbani
1
(Department of Mathematics, Shahrood University of Technology, Shahrood, Iran)
Keywords: energy, Eigenvalue of graph, Albertson Estrada index, Albertson energy,
Abstract :
‎Let $G$ 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.
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