Journal of Prime Research in Mathematics

# Analysis of closed neighbourhood indices of some Networks-II

B. Basavanagoud$$^{a,*}$$, Mahammad sadiq Sayyed$$^b$$

$$^a$$ Department of Mathematics, Karnatak University, Dharwad – 580 003, Karnataka, India

$$^b$$ Department of Mathematics, Karnatak University, Dharwad – 580 003, Karnataka, India

Correspondence should be addressed to: : b.basavanagoud@gmail.com

### Abstract

Topological indices are extensively used for establishing relationship between the chemical structure and their physico-chemical properties. Motivated by chemical applications of topological indices in the QSPR/QSAR analysis, we introduce a new topological indices that we call, second BM Index and fourth BM Index, is denoted by BM2(G) and BM4(G). Also we introduce second and fourth BM polynomials and is denoted by BM2(G, x) and BM4(G, x). In this paper, BM2(G) and BM4(G) is tested with physico-chemical properties of octane isomers such as entropy, acentric factor, enthalpy of vaporization (HVAP) and standard enthalpy of vaporization (DHVAP) using the linear models. The BM2(G) and BM4(G) shows excellent correlation with these chemical properties. Specially, BM2(G) and BM4(G) highly correlates with acentric factor (coefficient of correlation 0.9906546 and 0.9783643). Furthermore, we obtain BM2(G), BM4(G) indices and BM2(G, x), BM4(G, x) polynomials of dominating oxide network, regular triangulate oxide network, H-Naphtalenic nanotubes and nanocones of molecular graphs

#### Keywords:

BM indices, nanostructures, closed neighbourhood indices. 2010 MSC: 05C05, 05C12, 05C35.