On adjacency-distance spectral radius and spread of graphs

Haiyan Guo and Bo Zhou

Applied Mathematics and Computation, 2020, vol. 369, issue C

Abstract: Let G be a connected graph. The greatest eigenvalue and the spread of the sum of the adjacency matrix and the distance matrix of G are called the adjacency-distance spectral radius and the adjacency-distance spread of G, respectively. Both quantities are used as molecular descriptors in chemoinformatics. We establish some properties for the adjacency-distance spectral radius and the adjacency-distance spread by proposing local grafting operations such that the adjacency-distance spectral radius is decreased or increased. Hence, we characterize those graphs that uniquely minimize and maximize the adjacency-distance spectral radii in several sets of graphs, and determine trees with small adjacency-distance spreads. It transpires that the adjacency-distance spectral radius satisfies the requirements of a branching index.

Keywords: Adjacency-distance spectral radius; Adjacency-distance spread; Molecular descriptor; Branching index; Local grafting operation; Tree (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:369:y:2020:i:c:s0096300319308112

DOI: 10.1016/j.amc.2019.124819

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