Articles
Publication Date: 2025
Transactions On Combinatorics (22518657)14(3)pp. 157-172
As a real-valued function, a graphical parameter is defined on the class of finite simple graphs, and remains invariant under graph isomorphism. In mathematical chemistry, vertex-degreebased topological indices are the graph parameters of the general form of (Formula presented.), where ϕ represents a real-valued symmetric function, and d(u) shows the degree of u ∈ V (G). In this paper, it is proved that if ϕ has certain conditions, then the graph among those with n vertices and m edges, whose difference between the maximum and minimum degrees is at most 1, has the minimal value of pϕ. Moreover, it is demonstrated that some well-known topological indices are able to satisfy these certain conditions, and the given indices can be treated in a unified manner. © 2025 University of Isfahan
Publication Date: 2024
Iranian Journal Of Mathematical Chemistry (20089015)15(2)pp. 65-78
The Laplacian eigenvalues and polynomials of the networks play an essential role in understanding the relations between the topology and the dynamic of networks. Generally, computation of the Laplacian spectrum of a network is a hard problem and there are just a few classes of graphs with the property that their spectra have been completely computed. Laplacian spectrum for n-prism networks was investigated in [Liu et al., Neurocomputing 198 (2016) 69–73]. In this paper, we give a method for calculating the eigenvalues and characteristic polynomial of the Laplacian matrix of a generalized n-prism network. We show how such large networks can be constructed from small graphs by using graph products. Moreover, our results are used to obtain the Kirchhoff index and the number of the spanning trees in the generalized n-prism networks. We also give some examples of applications, that explain the usefulness and efficiency of the proposed method. © 2024 University of Kashan Press. All rights reserved.
Publication Date: 2024
Annales Mathematicae Silesianae (23914238)38(2)pp. 263-283
In this paper, we introduce the subset-strong product of graphs and give a method for calculating the adjacency spectrum of this product. In addition, exact expressions for the first and second Zagreb indices of the subset-strong products of two graphs are reported. Examples are provided to illustrate the applications of this product in some growing graphs and complex networks. ©2023 The Author(s).
