FIRST ZAGREB MATRIX AND ENERGY OF A T2 HYPERGRAPH

Sharmila D; Sujitha S; Angel Jebitha M K

doi:10.56827/SEAJMMS.2023.1902.17

Sharmila D Department of Mathematics, Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli - 627012, Tamil Nadu, INDIA
Sujitha S Department of Mathematics, Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli - 627012, Tamil Nadu, INDIA
Angel Jebitha M K PG and Research Department of Mathematics, Holy Cross College (Autonomous), Nagercoil, INDIA

DOI: https://doi.org/10.56827/SEAJMMS.2023.1902.17

Keywords: T2 hypergraph, first Zagreb matrix, first Zagreb energy.

Abstract

Let H be a T2 hypergraph of order n > 4. 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 di + dj if xi and xj 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 T2 hypergraph ZE(H) < l√ 2(n2+3n+1) √ 3 m .