On the maximal general ABC index of graphs with given maximum degree Articles uri icon

publication date

  • December 2020

start page

  • 1

end page

  • 12

issue

  • 125531

volume

  • 386

International Standard Serial Number (ISSN)

  • 0096-3003

Electronic International Standard Serial Number (EISSN)

  • 1873-5649

abstract

  • The atom-bond connectivity index ABC is a topological index that has recently found remarkable applications in the study of the strain energy of cycloalkanes as well as in rationalizing the stability of linear and branched alkanes. In order to improve the correlation
    properties of the atom-bond connectivity index for the heat of formation of alkanes, Furtula et al. considered a generalization of this index, namely,
    ABCα = ABCα (G) =
    uv∈E(G)
    du + dv − 2
    dudv
    α
    for any α ∈ R \ {0},
    where dv is the degree of the vertex v and uv denotes the edge connecting the vertices
    u and v of graph G. Here, we obtain some optimization results for ABCα of the connected
    graph G.

keywords

  • optimization problems; abc index; generalized abc index; degree-based topological indices