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BOSCH PÉREZ, PAUL JESÚS
Inequalities on the Generalized ABC Index
On the variable inverse sum deg index
CRIS - Current Research Information System
CRIS - Current Research Information System
2021
,
BOSCH PÉREZ, PAUL JESÚS
,
Edil D. Molina
,
José M. Rodríguez
,
José M. Sigarreta
In this work, we obtained new results relating the generalized atom-bond connectivity index with the general Randić index. Some of these inequalities for ABCα improved, when α=1/2, known results on the ABC index. Moreover, in order to obtain our results, we proved a kind of converse Hölder inequality, which is interesting on its own.
2023
,
Edil D. Molina
,
BOSCH PÉREZ, PAUL JESÚS
,
José M. Sigarreta
,
Eva Tourís
Several important topological indices studied in mathematical chemistry are expressed in the following way Puv∈E(G) F(du, dv), where F is a two variable function that satisfies the condition F(x, y) = F(y, x), uv denotes an edge of the graph G and du is the degree of the vertex u. Among them, the variable inverse sum deg index ISDa, with F(du, dv) = 1/(dua + dva), was found to have several applications. In this paper, we solve some problems posed by Vukičević [1], and we characterize graphs with maximum and minimum values of the ISDa index, for a < 0, in the following sets of graphs with n vertices: graphs with fixed minimum degree, connected graphs with fixed minimum degree, graphs with fixed maximum degree, and connected graphs with fixed maximum degree. Also, we performed a QSPR analysis to test the predictive power of this index for some physicochemical properties of polyaromatic hydrocarbons. © 2023 the Author(s), licensee AIMS Press.