The Minimum Incidence Energy of k-Uniform Hypergraphs

Abstract

For a $k$-uniform hypergraph ${\cal H} = \left( {V\left( {\cal H} \right),E\left( {\cal H} \right)} \right)$ of order $n = \left| {V({\cal H})} \right|$ and size $r = \left| {E({\cal H})} \right|$, let $B({\cal H})$ be the incidence matrix of ${\cal H}$.
The incidence energy $BE({\cal H})$ of ${\cal H}$ is the energy of $B({\cal H})$.
In this article, we determine the unique hypergraph with the minimum incidence energy among all $k$-uniform hypertrees of size $r$ with fixed number of pendent edges.We also determine the unique hypergraph with the minimum incidence energy
among all $k$-uniform unicyclic hypergraphs of size $r$.