**Journal of Prime Research in Mathematics**

Vol. 17 (2021), Issue 2, pp. 101 – 110

ISSN: 1817-3462E (Online) 1818-5495 (Print)

ISSN: 1817-3462E (Online) 1818-5495 (Print)

# Reciprocal leap indices of some wheel related graphs

**Swamy Javaraju\(^{a,*}\), Ammar Alsinai\(^a\), Anwar Alwardi\(^b\), Hanan Ahmed\(^c\), N. D. Soner\(^a\)**

\(^a\)Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysuru – 570 006, India.

\(^b\)Department of Mathematics, University of Aden, Yemen.

\(^c\)Department of Mathematics, Yuvaraja’s college, University of Mysore, India.

Correspondence should be addressed to: Swamy Javaraju at sgautham48@gmail.com

Copyright © 2021 Swamy Javaraju, Ammar Alsinai, Anwar Alwardi, Hanan Ahmed, N. D. Soner. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

**Published:**Received: 19 December 2020; Accepted: 30 July 2021; Published Online: 28 August 2021.

### Abstract

Recently, Ammar Alsinai et al., [1], introduced Reciprocal leap Zagreb indices of a graph based on the inverse second degree of vertices. The first Reciprocal leap Zagreb index \(RL_{1}(G)\) is equal to the sum of squares of the inverse second degrees of the vertices, the second Reciprocal leap Zagrab index \(RL_{2}(G)\) is equal to the sum of the products of the inverse second degrees of pairs of adjacent vertices of \(G\) and the third Reciprocal leap Zagreb \(RL_{3} \) is equal to the sum of the products of the inverse first degrees with the inverse second degrees of the vertices. In this paper, exact expression for Reciprocal leap Zagreb indices of wheel \(w_{n}\), and some related graphs as gear \(G_{n}\), helm \(H_{n}\), flower \(fl_{n}\) and sunflower \(sf_{n}\) graphs are commuted.

#### Keywords:

Second degree of vertex, Inverse degree, Leap Zagreb indices, Reciprocals leap indices, Wheel graphs.