Nordhaus–Gaddum-Type Relations for Arithmetic-Geometric Spectral Radius and Energy

Yajing Wang and Yubin Gao

Mathematical Problems in Engineering, 2020, vol. 2020, 1-7

Abstract:

Spectral graph theory plays an important role in engineering. Let be a simple graph of order with vertex set . For , the degree of the vertex , denoted by , is the number of the vertices adjacent to . The arithmetic-geometric adjacency matrix of is defined as the matrix whose entry is equal to if the vertices and are adjacent and 0 otherwise. The arithmetic-geometric spectral radius and arithmetic-geometric energy of are the spectral radius and energy of its arithmetic-geometric adjacency matrix, respectively. In this paper, some new upper bounds on arithmetic-geometric energy are obtained. In addition, we present the Nordhaus–Gaddum-type relations for arithmetic-geometric spectral radius and arithmetic-geometric energy and characterize corresponding extremal graphs.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:5898735

DOI: 10.1155/2020/5898735

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