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The forgotten index of hypergraphs and some hypergraph operations | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 11 شهریور 1404 اصل مقاله (439.25 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.30434.2466 | ||
| نویسندگان | ||
| Shashwath S Shetty؛ K Arathi Bhat* | ||
| Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal, 576104, Karnataka, India | ||
| چکیده | ||
| 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. | ||
| کلیدواژهها | ||
| Hyperstar؛ hyperpath؛ sunflower؛ Cartesian product؛ corona | ||
| مراجع | ||
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