https://doi.org/10.1140/epjp/s13360-022-03437-5
Regular Article
On Zagreb connection indices
1
Department of Mathematics, Sungkyunkwan University, 16419, Suwon, Republic of Korea
2
Department of Mathematics, National Institute of Technology Durgapur, 713209, Durgapur, West Bengal, India
3
Department of Mathematics, College of Sciences, University of Sharjah, 27272, Sharjah, UAE
Received:
28
September
2022
Accepted:
26
October
2022
Published online:
14
November
2022
Topological indices are numerical graph invariants that convert chemical structures into real numbers, allowing numerical computations to replace expensive wet lab experiments. The Zagreb connection indices attract considerable attention in a short period. The chain graph is a class of bipartite graphs in which the neighbors of the vertices belonging to each partite set form a chain in view of the set inclusion. We aim to explore the application potential of Zagreb connection indices and investigate their attractive mathematical features. The usefulness of the indices is established by analyzing the quantitative structure-property relationship and isomer discrimination ability. Tight upper bounds for three types of Zagreb connection indices are derived with identifying extremal graphs. Explicit expressions of the first Zagreb connection index, first modified Zagreb connection index, and second Zagreb connection index are derived for graphs having diameter two in terms of numerous graph parameters and well-known invariants. Crucial bounds of the Zagreb connection indices are set up for chain graphs, and corresponding extremal graphs are characterized.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
