Degree-based indices of hypergraphs: Definitions and first results

Abstract

For a [Formula: see text]-uniform hypergraph [Formula: see text], we introduce degree-based indices such as the general sum-connectivity index [Formula: see text] and the general Randić index [Formula: see text], where [Formula: see text], [Formula: see text] is the set of hyperedges of [Formula: see text] and [Formula: see text] is the degree of a vertex [Formula: see text] in [Formula: see text]; [Formula: see text] and [Formula: see text]. Other indices such as the first and second Zagreb index, first and second hyper-Zagreb index, classical sum-connectivity index, classical Randić index and harmonic index of a hypergraph [Formula: see text] are special cases of the general indices. For [Formula: see text], we obtain upper bounds on [Formula: see text] and [Formula: see text] for a uniform hypergraph [Formula: see text] with given order, order and number of isolated vertices, order and maximum degree, order and diameter at least [Formula: see text], and lower bounds for uniform hypergraphs with given order and no isolated vertices, order and minimum degree, and order and maximum possible degree. We also present extremal graphs for all the bounds. Bounds on Zagreb indices follow from our results on general indices.