Abstract

Let $H$ be a 3-uniform $T_2$ hypergraph with order $n\geq5$. The sum connectivity matrix of $H,$ denoted by SC(H) is defined as the square martix of order $n,$ whose $(i,j)^{th}$ entry is $\frac{1}{\sqrt{d_i+d_j}}$ if $x_i$ and $x_j$ are adjacent and zero for other cases. The sum connectivity energy SCE(H) of $H$ is the sum of the absolute values of the eigenvalues of SC(H). It is shown that, for a 3-uniform $T_2$ hypergraph $\left\lfloor SCE(H)\right\rfloor\leq \left\lfloor \frac{n}{2}\right\rfloor +2.$

Keywords and Phrases

$T_{2}$ hypergraph; 3-uniform $T_{2}$ hypergraph; sum connectivity matrix; sum connectivity energy.

A.M.S. subject classification

05C65.

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