﻿ Albertson energy and Albertson Estrada index of graphs

# Albertson energy and Albertson Estrada index of graphs

##### نویسنده
• A. Jahanbani Department of Mathematics, Shahrood University of Technology, Shahrood, Iran
##### چکیده

‎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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## Towards the Albertson Conjecture

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عنوان ژورنال:

دوره 08  شماره 01

صفحات  11- 24

تاریخ انتشار 2019-02-01

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