Volume: 55 Issue: 3
Year: 2024, Page: 12-16, Doi: https://doi.org/10.61649/kujos/v55i3.24.16
Received: July 24, 2024 Accepted: Aug. 26, 2024 Published: Sept. 12, 2024
The present research work introduces the concept of Laplacian energy with respect to block adjacency matrix named as Laplacian block adjacency energy. Further upper bound, lower bound and bound for spectral radius of Laplacian block adjacency energy are established for the graph with mutually adjacent blocks and helm graph.
Keywords: Block adjacency energy; Laplacian block adjacency energy; Spectral radius
Surekha. A study of inverse, mixed block domination and related concepts in graphs. Manipal Institute of Technology thesis
Gallian JA. Dynamic survey of graph labelling. The Electronic Journal of Combinatorics. 2018;17:1–502. Available from: https://www.combinatorics.org/files/Surveys/ds6/ds6v21-2018.pdf
Harary F. Graph theory. (pp. 1-284) Mass, Reading. Addison-Wesley. 1969.
Bernard S, Child JM. Higher Algebra. (pp. 1-605) New Delhi. Macmillan And Company Limited. 2001.
Gutman I. The Energy of a Graph. 103:1–22.
Cvetkovic DM, Doob M, Sachs H. Spectra of Graphs: Theory and Application. (pp. 1-447) Johann Ambrosius Barth. 1995.
Gutman I, Zhou B. Laplacian energy of a graph. Linear Algebra and its Applications. 2006;414(1):29–37. Available from: https://doi.org/10.1016/j.laa.2005.09.008
Mirajkar KG, Deshpande AV, Doddamani BR. On the bounds and energy of block adjacency matrix. Mathematical Forum. 2020;28(1):87–103. Available from: http://mathematical-forum.org/on-the-bounds-and-energy-of-block-adjacency-matrix-for-some-class-of-graphs/
I, Fortula GB. Graph energies and their applications, . Bulletin T. CLII de l’Acad´emie serbe des sciences et des arts − Classe des Sciences math´ematiques et naturelles Sciences math´ematiques,. 2019;44:29–45. Available from: http://elib.mi.sanu.ac.rs/files/journals/bltn/44/bltnn44p29-45.pdf
Zhou B. More on energy and Laplacian energy. MATCH Commun. Math. Comput. Chem. 2010;64:75–84. Available from: https://match.pmf.kg.ac.rs/electronic_versions/Match64/n1/match64n1_75-84.pdf
Keerthi G Mirajkar, Anuradha V Deshpande. On the Bounds for Laplacian Energy of Block Adjacency Matrix. Karnatak University Journal of Science 55(3), (2024), 12–16.