K Banhatti and K hyper Banhatti indices of circulant graphs

Abstract

A topological index is a numerical number associated with a graph that describes its topology. History traces a long path on the study of topological indices. A circulant graph is one of the most comprehensive families, as its specializations give some important families like complete graphs, crown graphs, rook graphs, complete bipartite graphs, cocktail party graphs, empty graphs, etc. The aim of this report is to compute the first and second K Banhatti indices of circulant graph. We also compute the first and second K hyper Banhatti indices of this family of graph. Moreover, we plot our results to see the dependences of the first and second K Banhatti indices and the first and second K hyper Banhatti indices on the involved parameters.

On the Metric Index of Circulant Networks–An Algorithmic Approach

“…They also constitute the basis for designing certain data alignment networks for complex memory systems [26]. Because of remarkable applications, circulant networks have been the subject of much investigations: the chromatic index [27], Connectivity [28], Wiener index [29], revised Szeged spectrum [30], M polynomial and many degree-based topological indices [31], first and second K Banhatti indices [32], some distance-based topological indices [33], [34] for circulant graphs are studied. In the context of metric index, Javaid et al [23] considered a family of circulant networks C n (1, 2) (also known as the Harary graph H 4,n ).…”

A Paradigmatic Approach to Find the Valency-Based K-Banhatti and Redefined Zagreb Entropy for Niobium Oxide and a Metal–Organic Framework

“…Because the work is derived from organized molecular motion, entropy is also a measure of a system’s molecular disorder or unpredictability [ 20 , 21 ]. In this article, we build the Niobium dioxide NbO and the metal–organic framework (MOF) to compute the K -Banhatti and redefined Zagreb entropies using K -Banhatti indices [ 22 , 23 , 24 ], and redefined Zagreb indices, respectively. The idea of entropy is extracted from Shazia Manzoor’s paper [ 25 ].…”

Some topological indices of dendrimers determined by their Banhatti polynomials

“…Further extension to this theory was made in 2017 when Kulli et al defined and computed connectivity K Banhatti indices including K harmonic Banhatti and multiplicative K harmonic Banhatti indices [16]. For more detail and theory about Banhatti indices, we refer the articles in [2,5,[16][17][18][19][20]24]. A huge amount of valency based topological indices and polynomials, defined and studied by various researchers, can be found in the literature (see [1,3,6,8,13,21,22,26] and the references therein).…”

“…In this paper, our first aim is to further extend the theory of Banhatti indices by defining four Banhatti polynomials. Moreover, we establish a few relationships of Banhatti indices, defined in (5) and (6), with the indices provided in (2), (3) and (4). Our second aim is to compute those valency based topological indices which can be determined by using the established relationships.…”