Abstract
The dependability and effectiveness of a network can be investigated using a variety of graph-theoretic techniques, and the network's connectivity determines how reliable it is. Diameter in a network is often used to measure the efficiency of a network in the event that a network experiences issues such as a decline in the communication signal or a breakdown in the communication between its components. This paper examines the increase in diameter of the generalized Petersen graph after removing a certain number of edges. Finding the exact values of f(n,t) that represent the maximum diameter of an altered generalized Petersen graph GP(n,k,t) obtained after removing edges from for k=1 and t≥2.
Reference7 articles.
1. B. Mahavir, “ Optimal book embedding of the generalized petersen graph p (n, 2) ”. International Conference on Mathematical Computer Engineering-ICMCE, pp 921-926, 2013.
2. S.A. Abdul-Ghani, R.D. Abdul-Wahhab and E.W. Abood , “Securing Text Messages Using Graph Theory and Steganography“. Baghdad Sci. J., Vol. 19, No. 1 , pp189-196,2022. http://dx.doi.org/10.21123/bsj.2022.19.1.0189 .
3. M.S. Krishnamoorthy and B. Krishnamurthy, “Fault diameter of interconnection networks”. , Computers & Mathematics with Applications, Elsevier, Vol. 13, pp 577—582 ,1987.
4. A. S Mary and P. Sivagamia, “On 3-rainbow Domination in Petersen graphs P (n, 2) and P (n, 3)”. International Conference on Mathematical Computer Engineering-ICMCE, pp 779-783 , 2013.
5. G. Chartrand, H. Hevia and R.J. Wilson , “The ubiquitous Petersen graph”. The Julius Petersen Graph Theory Centennial, North Holland, Vol.6, pp303—311, 1992.