### Multiplicative Revan and Multiplicative Hyper-Revan Indices of certain Networks

**V. R. Kulli**

Department of Mathematics,
Gulbarga University, Gulbarga 585106, INDIA.

email: vrkulli@gmail.com.

(Received on: December 3, 2017)

**ABSTRACT**

Recently, the Revan vertex degree concept was defined in Chemical Graph Theory. Furthermore, the Revan indices, connectivity Revan indices were introduced and studied well. In this paper, we propose the multiplicative Revan indices and determine exact formulae for oxide networks and honeycomb networks.

**Mathematics Subject Classification:** 05C05, 05C07, 05C12.

**Keywords:**Revan vertex degree, multiplicative Revan indices, multiplicative hyper- Revan indices, oxide network, honeycomb network.

**1.INTRODUCTION**

A topological index is a numerical parameter mathematically derived from the graph structure. Numerous topological indices have been considered in Theoretical Chemistry and many topological indices were defined by using vertex degree concept. The Zegreb, the Banhatti and the Gourava indices are the most degree based topological indices in Chemical Graph Theory. Very recently, Kulli1 defined a novel degree concept in graph theory: the Revan vertex degree and determined exact formulae for oxide and honeycomb networks.

** 2. RESULTS FOR OXIDE NETWORKS**

Oxide networks are very important in the study of silicate networks. A 5-dimensional
oxide network is depicted in Figure 1. An oxide network of dimension n is denoted by OX_{n}.

**3. RESULTS FOR HONEYCOMB NETWORKS**

Honeycomb networks are very useful in Chemistry and also in Computer Graphics. A honeycomb network of dimension n is denoted by HCn where n is the number of hexagons between central and boundary hexagon. A honeycomb network of dimension 4 is depicted in Figure 2.

**REFERENCES**

- V.R. Kulli, Revan indices of oxide and honeycomb networks, International Journal of Mathematics and its Applications, 5(4-E), 663-667 (2017).
- V.R. Kulli, College Graph Theory, Vishwa International Publications, Gulbarga, India (2012).
- V.R. Kulli, Hyper-Revan indices and their polynomials of silicate and hexagonal networks, submitted.
- V.R. Kulli, The sum connectivity Revan index of silicate and hexagonal networks, Annals of Pure and Applied Mathematics, 14(3), 401-406 (2017).

DOI: http://dx.doi.org/10.22457/apam.v14n3a6. - V.R. Kulli, Revan indices and their polynomials of certain rhombus networks, submitted.
- V.R. Kulli, On the product connectivity Revan index of certain nanotubes, Journal of Computer and Mathematical Sciences, 8(10), 562-567 (2017).
- V.R. Kulli, On K edge index of some nanostructures, Journal of Computer and Mathematical Sciences, 7(7), 373-378 (2016).
- V.R.Kulli, New K Banhatti topological indices, International Journal of Fuzzy Mathematical Archive, 12(1), 29-37 (2017). DOI:http://dx.doi.org/10.22457/ijfma. v12n1a4.
- V.R. Kulli, On the sum connectivity Gourava index, International Journal of Mathematical Archive, 8(7), 211-217 (2017).
- V.R. Kulli, The Gourava indices and coindices of graphs, Annals of Pure and Applied Mathematics, 14(1), 33-38 (2017). DOI:http://dx.doi-org/10.22457/apam.v14n1a4.
- V.R. Kulli, On the sum connectivity reverse index of oxide and honeycomb networks, Journal of Computer and Mathematical Sciences, 8(9), 408-413 (2017).
- V.R. Kulli, On the product connectivity reverse index of silicate and hexagonal networks, International Journal of Mathematics and its Applications, 5(4-B), 175-179 (2017).
- V.R. Kulli, Geometric-arithmetic reverse and sum connectivity reverse indices of silicate and hexagonal networks, International Journal of current Research in Science and Technology, 3(10), 29-33 (2017).
- V.R. Kulli, First multiplicative K Banhatti index and coindex of graphs, Annals of Pure and Applied Mathematics, 11(2), 79-82 (2016).
- V.R. Kulli, Multiplicative hyper-Zagreb indices and coindices of graphs: Computing these indices of some nanostructures, International Research Journal of Pure Algebra, 6(7), 342-347 (2016).
- V.R. Kulli, On multiplicative K-Banhatti and multiplicative K hyper-Banhatti indices of V-Phenylenic nanotubes and nanotorus, Annals of Pure and Applied Mathematics, 11(2), 145-150 (2016).
- V.R. Kulli, Multiplicative connectivity indices of TUC4C8[m,n] and TUC4[m,n] nanotubes, Journal of Computer and Mathematical Sciences, 7(11), 599-605 (2016).
- V.R. Kulli, On multiplicative connectivity indices of certain nanotubes, Annals of Pure and Applied Mathematics, 12(2), 169-176 (2016).
- V.R. Kulli, Multiplicative connectivity indices of nanostructures, Journal of Ultra Scientist of Physical Sciencs, A 29(1), 1-10 (2017).

DOI: http://dx.doi.org/10.22147/jusps.A/290101. - V.R. Kulli, Two new multiplicative atom bond connectivity indices, Annals of Pure and Applied Mathematics, 13(1), 1-7 (2017). DOI:http://dx.doi.org/10.22457/apam.vl3nlal.
- V.R. Kulli, Some new multiplicative geometric-arithmetic indices, Journal of Ultra Scientist of Physical Sciences, A, 29(2) (2017) 52-57.