SUM CONNECTIVITY MATRIX AND ENERGY OF A $T_2$ HYPERGRAPH
Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads : 99
DOI: https://doi.org/10.56827/SEAJMMS.2023.1903.27
Author :
Sharmila D. (Department of Mathematics, Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli, Tamil Nadu, INDIA)
Sujitha S. (PG and Research Department of Mathematics, Holy Cross College (Autonomous), Nagercoil, Tamil Nadu, INDIA)
Angel Jebitha M. K. (PG and Research Department of Mathematics, Holy Cross College (Autonomous), Nagercoil, Tamil Nadu, INDIA)
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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