20.500.12556/DKUM-93581 On the Wiener-like root-indices of graphs In this paper, we examine roots of graph polynomials where those roots can be considered as structural graph measures. More precisely, we prove analytical results for the roots of certain modified graph polynomials and also discuss numerical results. As polynomials, we use, e.g., the Hosoya, the Schultz, and the Gutman polynomial which belong to an interesting family of degree-distance-based graph polynomials; they constitute so-called counting polynomials with non-negative integers as coefficients and the roots of their modified versions have been used to characterize the topology of graphs. Our results can be applied for the quantitative characterization of graphs. Besides analytical results on bounds and convergence, we also investigate other properties of those measures such as their degeneracy which is an undesired aspect of graph measures. It turns out that the measures representing roots of graph polynomials possess high discrimination power on exhaustively generated trees, which outperforms standard versions of these indices. Furthermore, a new measure is introduced that allows us to compare different topological indices in terms of structure sensitivity and abruptness. graph theory Hosoya polynomial Schultz polynomial Gutman polynomial root-index discrimination power structure sensitivity teorija grafov korenski indeks diskriminacijska moč strukturna občutljivost true true true Springer Angleški jezik Slovenski jezik Znanstveno delo 2025-07-03 10:25:36 2025-07-03 10:25:37 2025-07-24 13:09:35 0000-00-00 00:00:00 2025 0 0 20 str. št. 7, št. članka 333 Letn. 44 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2025-03-10 2025-06-10 2025-06-28 519.17 241216515 10.1007/s40314-025-03296-7 1807-0302 RAZ_Brezovnik_Simon_2025.pdf RAZ_Brezovnik_Simon_2025.pdf 1 4FCE41AB5D52AC3A381C8CBD8599D63D 55fb041bec03f252d1957187d5f6e437b8808ac2240ed3b3a040280e86f9ce71 1c1eca7e-57e8-11f0-95d1-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=193216 https://doi.org/10.1007/s40314-025-03296-7 1 4fb4c31b-57e7-11f0-95d1-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=193213 Fakulteta za naravoslovje in matematiko 0 0 0