The forgotten index of hypergraphs and some hypergraph operations

Articles in Press

Document Type : Original paper

Authors

Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, 576104, Karnataka, India

Abstract

Hypergraphs generalize traditional graphs by allowing edges to connect more than two vertices, enabling a richer representation of relationships in complex systems. Forgotten topological index, or simply $F$-index of a hypergraph, is defined as the sum of cubes of the degrees of all the vertices of the hypergraph. Initially, some sharp bounds for the $F$-index of hypergraphs in terms of other degree-based topological indices have been obtained. A minimally connected hypergraph is a connected hypergraph such that the removal of any hyperedge disconnects the hypergraph. We have characterized the extremal minimally connected hypergraphs corresponding to the $F$-index among  minimally connected hypergraphs on $n$ vertices. The hyperstar and hyperpath with minimum and maximum $F$-indices have been studied. The upper and lower bounds for the $F$-index of the hypergraphs and bipartite hypergraphs are also given. We conclude this article by computing the $F$-index of join, corona product, and Cartesian product of two hypergraphs.

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References

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Communications in Combinatorics and Optimization

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Available Online from 02 September 2025

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