Vertex-Degree Function Index of Hypergraphs with Given Independence Number

Shetty, Shashwath S; Bhat, Arathi K

doi:10.22052/ijmc.2026.258204.2110

Vertex-Degree Function Index of Hypergraphs with Given Independence Number

Articles in Press

Document Type : Research Paper

Authors

Shashwath S Shetty ¹

Arathi K Bhat ²

¹ Manipal Institute of Technology Manipal Academy of Higher Education Manipal, India

² Manipal Institute of Technology Manipal Academy of Higher Education, Manipal, INDIA

10.22052/ijmc.2026.258204.2110

Abstract

Hypergraphs generalize graphs by permitting edges to link arbitrary numbers
of vertices, making them increasingly important for modeling complex networks.
Topological indices for hypergraphs offer critical insights into their structural properties
and complexity, with broad applications in network theory, chemistry, and data science.
This paper focuses on the vertex-degree function index of hypergraphs characterized by
a fixed independence number. We establish bounds for this index, generalizing classical
results from graph theory to hypergraphs. Specifically, by assuming convexity of the
function associated with the topological, we determine upper and lower bounds for the
vertex-degree function index of hypertrees and unicyclic hypergraphs with fixed independence
number.

Keywords

Vertex-degree

Independence number

Hypertrees

Unicyclic hypergraphs

Quality education

Subjects