Open AccessEnergy and Laplacian energy of unitary addition Cayley graphs
Author(s) -
Naveen Palanivel,
A. V. Chithra
Publication year - 2019
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1911599p
Subject(s) - mathematics , unitary state , complement (music) , laplace operator , cayley graph , prime (order theory) , eigenvalues and eigenvectors , combinatorics , graph , laplacian matrix , discrete mathematics , pure mathematics , mathematical analysis , chemistry , quantum mechanics , physics , biochemistry , complementation , political science , law , gene , phenotype
In this paper, we obtain the eigenvalues and Laplacian eigenvalues of the unitary addition Cayley graph Gn and its complement. Moreover, we compute the bounds for energy and Laplacian energy for Gn and its complement. In addition, we prove that Gn is hyperenergetic if and only if n is odd other than the prime number and power of 3 or n is even and has at least three distinct prime factors. It is also shown that the complement of Gn is hyperenergetic if and only if n has at least two distinct prime factors and n ? 2p.