Some results on the inverse sum indeg index of a graph

The inverse sum indeg index, which was selected in Vukičević (2010) [14] as a significant predictor of total surface area of octane isomers and for which the extremal graphs obtained with the help of MathChem have a particularly simple and elegant structure, is defined as ISI(G)=∑uv∈E(G)dudvdu+dv, where du is the degree of the vertex u of G. Recently, Falahati-Nezhad, Azari and Došlić (2017) [3] gave several sharp upper and lower bounds on this index in terms of some molecular structural parameters such as the order, size, radius, number of pendant vertices, minimal and maximal vertex degrees, and minimal non-pendent vertex degree, and related this index to several well-known molecular descriptors. In this paper, we present sharp bounds for the inverse sum indeg index for graphs with given matching number, independence number and vertex-connectivity, and we also characterize all extremal graphs for which those bounds are obtained.