Original Research Article

Article volume = 2021 and issue = 2

Pages: 120–128

Article publication Date: November, 1, 2021

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# Degree-Based Numerical Invariants of Grasmere Geometric Graph

#### M.C. Shanmukha(a), A. Usha(b)

(a)Department of Mathematics, Jain Institute of Technology, Davanagere-577003, Karnataka, India.

(b)Department of Mathematics, Alliance School of Applied Mathematics, Alliance University, Bangalore-562106, Karnataka, India

##### Abstract:

Graph theory plays a significant role in the applications of chemistry, pharmacy, communication, maps and aeronautical fields. This work is motivated by the old English tiles design on geometric structures, namely grasmere geometric tiles which are very popular in Victorian mosaic tiles. These are French manufactured tiles that have four different colours in it with dogtooth border. In this proposed work, the degree-based topological indices viz., Sombor index, Geometric-Harmonic index, Harmonic- Geometric index, SS index, RABC index, RABC4 index, neighborhood first Zagreb index, neighborhood second Zagreb index, neighborhood hyper Zagreb index, neighborhood third NDe index, neighborhood redefined first Zagreb index, neighborhood redefined second Zagreb index, generalized reciprocal Sanskruti index, neighborhood Sombor index and neighborhood SS index values are computed for grasmere geometric graph.

##### Keywords:

Grasmere Geometric graph, topological indices.

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##### Cite this article as:

- M.C. Shanmukha, A. Usha, Degree-Based Numerical Invariants of Grasmere Geometric Graph, Communications in Combinatorics, Cryptography & Computer Science, 2021(2), PP.120–128, 2021
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