Szeged and Mostar root-indices of graphs

Simon Brezovnik, Matthias Dehmer, Niko Tratnik and Petra Žigert Pleteršek

Applied Mathematics and Computation, 2023, vol. 442, issue C

Abstract: Various distance-based root-indices of graphs are introduced and studied in the present article. They are obtained as unique positive roots of modified graph polynomials. In particular, we consider the Szeged polynomial, the weighted-product Szeged polynomial, the weighted-plus Szeged polynomial, and the Mostar polynomial. We derive closed formulas of these polynomials for some basic families of graphs. Consequently, we provide closed formulas for some root-indices and examine the convergence of sequences of certain root-indices. Moreover, some general properties of studied root-indices are stated. Finally, numerical results related to discrimination power, correlations, structure sensitivity, and abruptness of root-indices are calculated, interpreted, and compared to already known similar descriptors.

Keywords: Szeged index; Szeged polynomial; Mostar polynomial; Root-index; Discrimination power; Sensitivity (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:442:y:2023:i:c:s0096300322008049

DOI: 10.1016/j.amc.2022.127736

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