A Study On The Number Of Edges Of Some Families Of Graphs And Generalized Mersenne Numbers

K.G. Sreekumar, Ramesh Kumar P., K Manilal


The relationship between the Nandu sequence of the SM family of graphs and the generalized Mersenne numbers is demonstrated in this study. The sequences obtained from the  peculiar number of edges   of SM family of  graphs are known as Nandu sequences. Nandu sequences are related to the two families of SM sum graphs and SM balancing graphs. The SM sum graphs are established from the inherent relationship between powers of 2 and natural numbers, whereas the SM balancing graphs are linked to the balanced ternary number system.  In addition, some unusual prime numbers are discovered in this paper. These prime numbers  best suit as an alternate for the Mersenne primes in the case of the  public key cryptosystem.


SM Balancing graphs, SM Sum graphs, Nandu Sequence, Generalized Mersenne numbers, SM prime numbers

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DOI: http://dx.doi.org/10.23755/rm.v42i0.704


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