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IMI/Publicaţii/CSJM/Ediţii/CSJM v.29, n.2 (86), 2021/

Bounds for Degree-Sum adjacency eigenvalues of a graph in terms of Zagreb indices

Authors: Sumedha S. Shinde, Narayan Swamy, Shaila B Gudimani, H. S. Ramane
Keywords: Adjacency eigenvalues, degree sum adjacency matrix, Zagreb index, Eigenvalues, Energy.

Abstract

For a graph $G$ the degree sum adjacency matrix $DS_A(G)$ is defined as a matrix, in which every element is sum of the degrees of the vertices if and only if the corresponding vertices are adjacent, otherwise it is zero. In this paper we obtain the bounds for the spectral radius and partial sum of the eigenvalues of the $DS_A$ matrix. We also find the bounds for the $DS_A$ energy of a graph in terms of its Zagreb indices.

Sumedha S. Shinde
Depathment of Mathematics,
KLE Technological University,
Hubballi-580031, India
Phone: 9448631697
E-mail:

Narayan Swamy
Depathment of Mathematics,
KLE Technological University,
Hubballi-580031, India
Phone: 9448631697
E-mail:

Shaila Gudimani
Depathment of Mathematics,
KLE Technological University,
Hubballi-580031, India
Phone: 9448631697
E-mail:

Harishchandra S. Ramane
Department of Mathematics,
Karnatak University,
Dharwad - 580003, India
Phone: +919945031752
E-mail:

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