Small-World Networks with Unitary Cayley Graphs for Various Energy Generation C. Thilaga, P. B. Sarasija Computer Systems Science and Engineering, 2023 Complex networks have been a prominent topic of research for several years, spanning a wide range of fields from mathematics to computer science and also to social and biological sciences. The eigenvalues of the Seidel matrix, Seidel Signless Laplacian matrix, Seidel energy, Seidel Signless Laplacian energy, Maximum and Minimum energy, Degree Sum energy and Distance Degree energy of the Unitary Cayley graphs [UCG] have been calculated. Low-power devices must be able to transfer data across long distances with low delay and reliability. To overcome this drawback a small-world network depending on the unitary Cayley graph is proposed to decrease the delay and increase the reliability and is also used to create and analyze network communication. Small-world networks based on the Cayley graph have a basic construction and are highly adaptable. The simulation result shows that the small-world network based on unitary Cayley graphs has a shorter delay and is more reliable. Furthermore, the maximum delay is lowered by 40%.
THE SEIDEL LAPLACIAN ENERGY OF UNITARY CAYLEY GRAPHS C. Thilaga, P. B. Sarasija Missouri Journal of Mathematical Sciences, 2022 The Seidel Laplacian matrix of the Unitary Cayley graph Xn is SL(Xn)=DS(Xn)-S(Xn). In this paper, we obtain the eigenvalues of the Seidel Laplacian matrix and the Seidel Laplacian Energy of Unitary Cayley Graphs Xn.
Wiener and hyper–wiener indices of unitary addition cayley graphs Ante Graovac, Toma Pisanski, A Graovac, T Pisauski, D Grynkiewicz, et al. International Journal of Recent Technology and Engineering, 2019 A topological index is a number associated to a graph. In chemical graph theory the Wiener index of a graph G, denoted by W(G) is the sum of the distance between all (unordered) pairs of vertices of G. That is, W(G) = ,where d (ui , uj) is the shortest distance between the vertices. ui and uj .The Hyper-Wiener Index WW(G) is the generalization of the Wiener index. The Hyper- Wiener Index of a graph G is, WW (G) = .The unitary addition Cayley graph Gn has a vertex set Zn = {0, 1,…, n-1} and the vertices u and v are adjacent if gcd (u+v,n) =1. In this paper Wiener index and Hyper Wiener indices of Unitary addition Cayley graph Gn is computed
