SUM CONNECTIVITY MATRIX AND ENERGY OF A $T_2$ HYPERGRAPH

Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads : 47

Abstract

Let $H$ be a $T_2$ hypergraph with $n\geq4.$ 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 $T_2$ hypergraph $\left\lfloor SCE(H)\right\rfloor\leq \left\lfloor 1+n-{\sqrt{\frac{n}{\delta}}}\right\rfloor,$where $\delta$ is the minimum degree of $H$.

Keywords and Phrases

$T_{2}$ hypergraph, sum connectivity matrix, sum connectivity energy.

A.M.S. subject classification

05C65, 05C50.

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