Bounds on the Path Energy

Year 2020, Issue: 30, 64 - 68, 26.03.2020

Gülistan Kaya Gök

Abstract

In this paper, the path energy for path matrix is investigated. Some bounds for the path energy in terms of the eigenvalues and the vertices are explored.

Also, some relations are obtained for tree connected graphs.

Keywords

path matrix , path energy

References

• S. C. Patekar M.M. Shikare, On the path matrices of graphs and their properties, Adv. Appl. Discr. Math. 17 (2016) 169-184.
• S. Akbari, A.H. Ghodrati, I. Gutman, M.A. Hosseinzadeh, E.V. Konstantinova, On Path Energy of Graphs, MATCH Commun. Math. Comput. Chem. 81 (2019) 465-470.
• M.M. Shikare, P.P. Malavadkar, S.C. Patekar and I. Gutman, On path eigenvalues and path energy of graphs, MATCH Commun. Math. Comput. Chem. 79 (2018) 387-398.
• A. Lupas, A remark on the Schweitzer and Kantorovich Inequalities, Publikacije Elektrotehni\v{c}kog Fakulteta, Serija Matematika i Fizika, 381-409 (1972) 13-15.
• P. Cerone, S.S. Dragomir, A refinement of the Gruss inequality and applications,Tamkang J. Math. 38 (1) (2007) 39-49.
• R.B. Bapat, Graphs and Matrices, Indian Statistical Institute, New Delhi 110016, India.
• S. Büyükköse, G. Kaya Gök, Graf Teoriye Giris, Nobel Akademik Yay. Egitim Dan. Tic.Ltd.Sti, Ankara, (2018).
• G. Kaya Gök, Some bounds on the distance-sum-connectivity matrix, Journal of Inequalities and Applications 2018 171.