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

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  • Yajing Wang
  • Yubin Gao

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.

Suggested Citation

  • Yajing Wang & Yubin Gao, 2020. "Nordhaus–Gaddum-Type Relations for Arithmetic-Geometric Spectral Radius and Energy," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-7, July.
    • Handle: RePEc:hin:jnlmpe:5898735
    DOI: 10.1155/2020/5898735
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    Cited by:

    1. Zheng, Ruiling & Su, Peifeng & Jin, Xian’an, 2023. "Arithmetic-geometric matrix of graphs and its applications," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    2. Ganie, Hilal A., 2021. "On the distance Laplacian energy ordering of a tree," Applied Mathematics and Computation, Elsevier, vol. 394(C).

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