Graph Topological Indices and Energies of a Mixed Hourglass Graph.

Abstract:

Spectral graph theory has witnessed the development of topological indices based on degrees as effective methods of graph structure analysis, particularly in terms of graph energies. The current work explores degree-weighted spectral invariants (Nirmala and Sombor energies) on the mixed hourglass graph, which is topologically synthesized as a structure arising from the mixed adjacency representation of the WH factorization. The mixed hourglass graph is introduced as the graph containing both undirected edges and arcs, of which the vertex degrees serve as the central concept in terms of constructing the Nirmala and Sombor matrices. The relationship between the Nirmala and Sombor energies is the similarity between their graph spectra, and that the energies are even.