The Generalized Zagreb Index of Capra Operation on Cycle

Keerthi G. Mirajkar¹ , Pooja B² , M. R. Farahani³

Section:Research Paper, Product Type: Isroset-Journal
Vol.6 , Issue.1 , pp.251-254, Feb-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i1.251254

Online published on Feb 28, 2019

Copyright © Keerthi G. Mirajkar, Pooja B, M. R. Farahani . 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.
 

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Abstract :
The Generalized Zagreb index of a graph G is defined for arbitrary non-negative integer r and s as M_((r,s)) (G)=∑_(uv∈E(G) )▒‍[d_G^r (u)d_G^s (v)+d_G^s (u)d_G^r (v)]. In this paper, we obtain expressions for generalized Zagreb index of Capra operation of cycle C_n on n vertices, which generalizing the existing results of Sardar et al. (Open J. Math. Sci. 1 (2017) 44-51). As an application, this result enables us to find first Zagreb index, second Zagreb index and F-index of Capra operation of cycle C_n on n vertices.

Key-Words / Index Term :
Capra Operation, Generalized Zagreb Index

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