The spectral polynomials of two joining graphs: splices and links
Résumé
Energy of a graph, firstly defined by E. Hückel as the sum of absolute values of the eigenvalues of the adjacency matrix, in other words the sum of absolute values of the roots of the characteristic (spectral) polynomials, is an important sub area of graph theory. Symmetry and regularity are two important and desired properties in many areas including graphs. In many molecular graphs, we have a pointwise symmetry, that is the graph corresponding to the molecule under investigation has two identical subgraphs which are symmetrical at a vertex. Therefore, in this paper, we shall study only the vertex joining graphsIn this article we study the characteristic polynomials of the two kinds of joining graphs called splice and link graphs of some well known graph classes.
Téléchargements
Références
Aldous, J. M., Wilson, R. J., Graphs and Applications, The Open University, UK, 2004
Ashrafi, A. R., Hamzeh, A., Hossein-Zadeh, S., Calculation of Some Topological Indices of Splices and Links of Graphs, J. Appl. Math & Informatics 29 (1-2) (2011), 327-335
Brouwer, A. E., Haemers, W. H., Spectra of Graphs, Springer, New York, 2012 https://doi.org/10.1007/978-1-4614-1939-6
Celik, F., Cangul, I. N., Formulae and Recurrence Relations on Spectral Polynomials of Some graphs, Advanced Studies in Contemporary Mathematics 27 (3) (2017), 325-332
Celik, F., Cangul, I. N., Some Recurrence Relations for the Energy of Cycle and Path Graphs, Proceedings of the Jangjeon Mathematical Society, 21 (3) (2018), 347-355
Cvetkovic, D., Doob, M., Sachs, H., Spectra of Graphs-Theory and Applications (Third edn.), Academic Press, Heidelberg, 1995
Doslic, T., Splices, Links, and Their Valence-Weighted Wiener Polynomials, Graph Theory Notes, New York 48 (2005), 47-55
Li, X., Shi, Y., Gutman, I., Graph Energy, Springer, New York, 2012 https://doi.org/10.1007/978-1-4614-4220-2
Copyright (c) 2022 Boletim da Sociedade Paranaense de Matemática
Ce travail est disponible sous la licence Creative Commons Attribution 4.0 International .
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
