FIRST ZAGREB MATRIX AND ENERGY OF A $T_2$ HYPERGRAPH
Print ISSN: 0972-7752 | Online ISSN: 2582-0850 | Total Downloads : 126
DOI: https://doi.org/10.56827/SEAJMMS.2023.1902.17
Author :
Sharmila D. (Department of Mathematics, Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli - 627012, Tamil Nadu, INDIA)
Sujitha S. (PG and Research Department of Mathematics, Holy Cross College (Autonomous), Nagercoil, INDIA)
Angel Jebitha M. K. (PG and Research Department of Mathematics, Holy Cross College (Autonomous), Nagercoil, INDIA)
Abstract
Let $H$ be a $T_2$ hypergraph of order $n\geq4$. The first Zagreb matrix of $H$, denoted by $Z(H)$ is defined as the square matrix of order $n$, whose $(i,j)^{th}$ entry is $d_i+d_j$ if $x_i$ and $x_j$ are adjacent and zero for other cases. The first Zagreb energy $ZE(H)$ of $H$ is the sum of the absolute values of the eigenvalues of $Z(H)$. It is shown that, for a $T_2$ hypergraph $ZE(H)\leq\left\lceil\frac{\sqrt{2}(n^2+3n+1)}{\sqrt{3}}\right\rceil.$
Keywords and Phrases
$T_{2}$ hypergraph, first Zagreb matrix, first Zagreb energy.
A.M.S. subject classification
05C65, 05C50.
.....
