M-polynomial and related degree-based topological indices of the third type of chain Hex-derived network

Abstract

In chemical graph theory, a topological index is a numerical descriptor that describes the various biological activities, physical properties and chemical reactivities of molecular graphs. Recent studies compute several degree-based topological indices of a graph network by deriving its M-polynomial. In this paper, we would like to find out a closed form of M-polynomial for the third type of chain Hex-derived network of dimension n and hence derive various degree-based topological indices. Further, we plot the M-polynomial and all the related degree-based topological indices of the above network for different dimensional values.

On Nirmala Indices of Some Hex-derived Networks of Type Three and Their Subdivision Networks

“…Using this fundamental subdivision procedure on the HDN3[n], THDN3[n], RHDN3[n] and CHDN3[n] networks, one can have a subdivided hex-derived network of third type of dimension n (symbolized as SHDN3 [n], see Figure 1(b) for SHDN3 [3]), subdivided triangular hexderived network of third type of dimension n (symbolized as STHDN3[n], see Figure 2(b) for STHDN3 [4]), subdivided rectangular hex-derived network of third type of dimension n (symbolized as SRHDN3[n], see Figure 3(b) for SRHDN3 [4]) and subdivided chain hex-derived network of third type of dimension n (symbolized as SCHDN3 [n], see Figure 4(b) for SCHDN3 [5]). Please see [8,10,29,30] and their references therein for more detailed structural information.…”

On the Hosoya polynomial of the third type of the chain hex-derived network

“…Besides this, Raj et al [32] designed some new chemical networks from the hexagonal network of dimension n in 2017, called hex-derived networks of the third type. Taking into account the chain silicate network [33] and the third type of the hex-derived network [32], a chain hex-derived network of the third type of dimension 1 n (CHDN3[n]) has been constructed (for a detailed drawing algorithm of the CHDN3[n] network, please refer to [34]). An example of the third type of chain hex-derived network of dimension 5 (i. e., CHDN3 [5]) is shown in fig.…”

“…In reference [35], various degree-based topological indices of the CHDN3[n] network are calculated with the help of their direct formulas. Whereas, very recently in reference [34], the same was derived by using the M-polynomial of the CHDN3[n] network and one also plotted the topological indices and the M-polyno mial to understand their mathematical characteristics. Also, in reference [36], the structure of the subdivided hex-derived network of the third type of dimension n (SHDN3[n]) was designed and its M-polynomial and corresponding topological indices were estimated.…”

Neighborhood degree sum-based molecular indices and their comparative analysis of some silicon carbide networks

“…In 2015, Deutsch and Klažar established the M-polynomial to compute various degree-based topological indices [10]. In [11][12][13][14][15][16][17][18], some well-known degree-based topological indices of a variety of chemical compounds and networks are obtained with the help of their M-polynomials. Furthermore, the M-polynomial-based derivation formulas to compute the Nirmala and GQ-QG indices and their computation for different chemical networks were reported in [2,19,20].…”