DEGREE FACTORIAL ENERGY OF HYDROCARBON GRAPHS AND BENZENOID SYSTEM
Keywords:
Degree factorial matrix of molecular graph, Degree factorial polynomial and Degree factorial energy of molecular graph, Polycyclic Aromatic hydrocarbons (PAHn), hydrogen depleted polycyclic aromatic hydrocarbon HDPAHn, Fullerene graph, Benzenoid system, Log PAbstract
In this paper, we explore the degree factorial characteristic polynomial and the degree factorial energy of three types of hydrocarbons—Alkanes, Alkenes, and Alkynes. We investigate the relationship between the molar mass of these hydrocarbons and the degree factorial energy of their corresponding molecular graphs. Additionally, we examine the relationship between the degree factorial energy of Alkanes, Alkenes, and Alkynes.
We further study the degree factorial characteristic polynomial and energy of polycyclic aromatic hydrocarbons (PAHs), including hydrogen-depleted PAHs, and analyze the correlation between them. The degree factorial energy of Fullerene graphs and their variants is discussed by introducing degree factorial energy for r-regular graphs. We also derive upper and lower bounds for the degree factorial energy of simple graphs with n vertices, and the degree factorial energy for various Benzenoid systems such as Jagged Rectangular Benzenoids, Triangular Benzenoid systems, Zigzag Benzenoids, and Concealed non-Kekulean Benzenoids.
We introduce Degree Factorial Energy (DFE) as a novel molecular descriptor, demonstrating a linear correlation with Log P, thereby offering insights into the prediction of molecular lipophilicity. Additionally, the degree factorial energy of standard graph families such as path graphs, cycle graphs, complete graphs, grid graphs, wheel graphs, star graphs, and triangular snake graphs were obtained in [5]
