Distance powers of unitary Cayley graphs

Graphs Defined on Rings: A Review

“…It was observed that the kernel radius of X n is a strictly decreasing function on the range 0, n 2 . Apart from this, computation of certain graph parameters of the unitary Cayley graph were carried out in [86][87][88][89][90][91][92][93]; certain topological indices of the unitary Cayley graphs were computed in [90][91][92], and a few graph polynomials for the unitary Cayley graphs were determined in [86], using the results that were given in [54], as graph polynomials are also graph invariants that code numerical information about the underlying graph (c.f. [94]).…”

Eigenvalues of Cayley graphs

“…In particular, for any positive integer k, G {1,2,...,k} is called the kth power of G and is usually denoted by G k . The second power G 2 is usually called the square of G. Recently, Liu and Li [212] studied distance powers of the unitary Cayley graph Cay(Z n , Z × n ). Since Cay(Z n , Z × n ) is integral, by Theorem 3.8, such distance powers are all integral circulant graphs.…”

“…In view of Theorem 3.8, all distance powers of the unitary Cayley graph G Zn (= Cay(Z n , Z × n ) = ICG(n, {1})) are integral circulant graphs. The energies of some distance powers of G Zn were computed by Liu and Li in [212] and as a consequence when such a distance power is hyperenergetic was determined. Theorem 6.…”

“…Recently, Liu and Li [212] considered some distance powers of the unitary Cayley graph G Zn and determined when they are Ramanujan.…”

The Energy of Cayley Graphs for a Generating Subset of the Dihedral Groups

“…Meanwhile, the properties that the energy of a graph is never the square root of an odd integer has been proven by Pirzada and Gutman [4] in 2008. There are also a few other researchers who studied specifically on the energy of unitary Cayley graphs (see [5], [6]).…”