30 research outputs found
Author Correction: Divorce prediction using machine learning algorithms in Ha’il region, KSA
No full textOn the maximum atom-bond sum-connectivity index of graphs
No full textThe atom-bond sum-connectivity (ABS) index of a graph GG with edges e1,…,em{e}_{1},\ldots ,{e}_{m} is the sum of the numbers 1−2(dei+2)−1\sqrt{1-2{\left({d}_{{e}_{i}}+2)}^{-1}} over 1≤i≤m1\le i\le m, where dei{d}_{{e}_{i}} is the number of edges adjacent to ei{e}_{i}. In this article, we study the maximum values of the ABS index over graphs with given parameters. More specifically, we determine the maximum ABS index of connected graphs of a given order with a fixed (i) minimum degree, (ii) maximum degree, (iii) chromatic number, (iv) independence number, or (v) number of pendent vertices. We also characterize the graphs attaining the maximum ABS values in all of these classes
Existence and uniqueness of neutral functional differential equations with sequential fractional operators
No full textOn the Existence and Ulam Stability of BVP within Kernel Fractional Time
No full textThis manuscript, we establish novel findings regarding the existence of solutions for second-order fractional differential equations employing Ψ-Caputo fractional derivatives. The application of Banach’s fixed-point theorem (BFPT) ensures the uniqueness of the solutions, while Schauder’s fixed-point theorem (SFPT) is instrumental in determining the existence of these solutions. Furthermore, we assess the stability of the proposed equation using the Ulam–Hyers stability criterion. To illustrate our results, we provide a concrete example showcasing their practical implications
Novel Contributions to the System of Fractional Hamiltonian Equations
No full textThis work aims to analyze a new system of two fractional Hamiltonian equations. We propose an effective method for transforming the established model into a system of two distinct equations. Two functionals that are connected to the converted system of fractional Hamiltonian systems are introduced together with a new space, and it is demonstrated that these functionals are bounded below on this space. The hypotheses presented here differ from those provided in the literature
On the Maximum Atom-Bond Sum-Connectivity Index of Graphs
No full textThe atom-bond sum-connectivity (ABS) index of a graph with edges
is the sum of the numbers over
, where is the number of edges adjacent with . In
this paper, we study the maximum values of the ABS index over graphs with given
parameters. More specifically, we determine the maximum ABS index of connected
graphs of a given order and with a fixed (i) minimum degree, (ii) maximum
degree, (iii) chromatic number, (iv) independence number, or (v) number of
pendent vertices. We also characterize the graphs attaining the maximum ABS
values in all of these classes.Comment: 12 pages, no figur
On-Bond Incident Degree Indices of Square-Hexagonal Chains
No full textFor a graph G, its bond incident degree (BID) index is defined as the sum of the contributions fdu,dv over all edges uv of G, where dw denotes the degree of a vertex w of G and f is a real-valued symmetric function. If fdu,dv=du+dv or dudv, then the corresponding BID index is known as the first Zagreb index M1 or the second Zagreb index M2, respectively. The class of square-hexagonal chains is a subclass of the class of molecular graphs of minimum degree 2. (Formal definition of a square-hexagonal chain is given in the Introduction section). The present study is motivated from the paper (C. Xiao, H. Chen, Discrete Math. 339 (2016) 506–510) concerning square-hexagonal chains. In the present paper, a general expression for calculating any BID index of square-hexagonal chains is derived. The chains attaining the maximum or minimum values of M1 and M2 are also characterized from the class of all square-hexagonal chains having a fixed number of polygons
