Small-World Networks with Unitary Cayley Graphs for Various Energy Generation

Abstract

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%.

Graphs Defined on Rings: A Review

“…The eigenvalues of the A L matrix, defined with respect to the proper colourings of the graphs, were examined, and the corresponding energy was obtained in terms of the chromatic number of the graph and the Euler totient function, using the notion of Ramanujan Sums. A study on a few other matrices of the unitary Cayley graphs, along with their eigenvalues and energy, was conducted in [81], where a small-world network depending on the unitary Cayley graph was proposed, with an intent to decrease the delay and increase the reliability in data transfer used to create and analyse network communication.…”