Eccentric Harmonic Index for the Cartesian Product of Graphs

Abstract

Suppose ρ is a simple graph, then its eccentric harmonic index is defined as the sum of the terms 2 / e a + e b for the edges v a v b , where e a is the eccentricity of the a th vertex of the graph ρ . We symbolize the eccentric harmonic index (EHI) as H e = H e ρ . In this article, we determine H e for the Cartesian product (CP) of particularly chosen graphs. Lower bounds for H e of the CP of the two graphs are established. The formulas of EHI for the Hamming and Hypercube graphs are obtained. These obtained formulas can be used in QSAR and QSPR studies to get a better understanding of their applications in mathematical chemistry.

Further study of eccentricity based indices for benzenoid hourglass network

“…In this network there are types of vertices on neighborhood degree based and types of vertices based on and for where . We can construct tables of this network for computing different topological indices [ 18 , 19 ] and also their polynomials, in the product of degrees of all neighborhood vertices of vertex , is the sum of degrees of all neighborhood vertices of vertex , and their respective polynomials. Table [1] shows vertex degree based calculations with respect to eccentricity, and their count respectively.…”

Graphical Invariants for some Transformed Networks

“…In this paper, certain degree based topological indices [1,2,[18][19][20][21][25][26][27], namely; general Randic index, sum connectivity index, general sum connectivity index, first, second and third Zagreb indices, atomic bond connectivity index, geometric arithmetic index, general version of harmonic index are computed for transformed structures by applying stellation and bounded dual operations, derived networks are named G 1 and G 2 . Analytically closed formulae of above mentioned topological indices for these networks are stated.…”

“…Hayat et al calculated some degree-based topological indices of certain nanotubes and networks [11], [14]. Few networks are discussed in [16], [13], [12], [42], [29], [15], [23]. Ma et al studied the energy and operations of graphs [28].…”

Topological Characterization of Hexagonal Network and Non-Kekulean Benzenoid Hydrocarbon

“…In chemistry, a graph is a natural representation of a molecule, with vertices representing atoms and edges signifying bonds. For certain nanostructures their ABC and GA indices for this critical class of networks are studied in [10,23,24]. One can also see the literature related to structural invariants of graphs in [3,6,12,13,16,17,21,25,32].…”