Abstract
The general sum-connectivity index chi(alpha) of a graph G is defined as chi(alpha)(G) = Sigma(uv is an element of(G))(d(u) + d(v))(alpha), where uv is the edge connecting the vertices u and v, d(u) is the degree of the vertex u, and alpha is a real number. Research on chi(alpha) began in 1972, when the first Zagreb index chi(1) was introduced within a study of total pi-electron energy. Later, in 1987, the harmonic index H(= 2(chi-1)) appeared in connection with some conjectures, generated by the computer program Graffiti. The sum-connectivity index chi(-1/2), was proposed in 2009 and eventually extended to the general sum-connectivity index chi(alpha), which not only includes all the aforementioned graph invariants but also the hyper-Zagreb index chi(2). In this survey, we outline extremal results and bounds involving the mentioned invariants.