Extremal Zagreb indices of bicyclic hypergraphs

TL;DR

This paper investigates the extremal values of Zagreb indices in linear bicyclic hypergraphs, identifying those with the maximum and minimum indices among all such hypergraphs.

Contribution

It determines the hypergraphs with extremal Zagreb indices within the class of linear bicyclic uniform hypergraphs, a novel characterization in hypergraph theory.

Findings

Identified hypergraphs with maximum Zagreb index

Identified hypergraphs with minimum Zagreb index

Provided formulas for extremal values

Abstract

The Zagreb index of a hypergraph is defined as the sum of the squares of the degrees of its vertices. A connected $k$-uniform hypergraph with $n$ vertices and $m$ edges is called bicyclic if $n=m(k-1)-1$. In this paper, we determine the hypergraphs with the maximum and minimum Zagreb indices among all linear bicyclic uniform hypergraphs.