On bounds for the atom bond sum connectivity index of graphs associated with symmetric numerical semigroups

The computation of the clique number of a graph is a fundamental problem in graph theory, which has many applications in computational chemistry, bioinformatics, computer, and social networking. A subset [Formula: see text] of non-negative integers [Formula: see text] is called a numerical semigroup if it is a submonoid of [Formula: see text] and has a finite complement in [Formula: see text]. The graph associated with numerical semigroup [Formula: see text] is denoted by [Formula: see text] and is defined by the vertex set [Formula: see text] and the edge set [Formula: see text]. In this article, we compute the clique number and the minimum degree of those graphs, which can be associated with symmetric numerical semigroups of embedding dimension 2. Moreover, on this basis, we give some bounds for the atom-bond sum-connective index of graphs [Formula: see text] in terms of the harmonic index, the first Zagreb index, the sum-connectivity index, the maximum degree, the minimum degree, the chromatic number, and the clique number.