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Graph invariants of the line graph of zero divisor graph of \(\mathbb {Z}_{n}\)

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Abstract

Graph invariants provide an outstanding tool for investigation of abstract structures of graphs. They contain global and general information about a graph and its particular substructures. In this paper, the graph invariants such as vertex connectivity, metric dimension, minimum vertex degree, independence number, domination number, Laplacian energy and Zagreb indices of line graph of zero-divisor graph over the rings \(\mathbb {Z}_{pq}\) and \(\mathbb {Z}_{p^n}\) (where p and q are prime) are determined. Moreover, we provide a MATLAB code for calculating Laplacian energy and Zagreb indices of line graph of \(\varGamma (\mathbb {Z}_{n})\).

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Acknowledgements

We would like to thank the reviewers for their valuable comments and suggestions towards improving our manuscript.

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  1. School of Mathematics, Shri Mata Vaishno Devi University, Katra, Jammu and Kashmir, 182320, India

    Pradeep Singh & Vijay Kumar Bhat

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  1. Pradeep Singh
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  2. Vijay Kumar Bhat
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Correspondence to Vijay Kumar Bhat.

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Singh, P., Bhat, V.K. Graph invariants of the line graph of zero divisor graph of \(\mathbb {Z}_{n}\). J. Appl. Math. Comput. 68, 1271–1287 (2022). https://doi.org/10.1007/s12190-021-01567-0

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  • DOI: https://doi.org/10.1007/s12190-021-01567-0

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