Ratio Mathematica (Jun 2022)

A study on the number of edges of some families of graphs and generalized Mersenne numbers

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

DOI
https://doi.org/10.23755/rm.v42i0.704
Journal volume & issue
Vol. 42, no. 0
pp. 61 – 72

Abstract

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The relationship between the Nandu sequence of the SM family of graphs and the Generalized Mersenne numbers is demonstrated in this study. Nandu sequences are related to the two families of SM sum graphs and SM Balancing graphs. The SM sum graphs are linked to the inherent relationship between powers of 2 and natural numbers, whereas the SM balancing graphs are linked to the balanced ternary number system. The peculiar number sequences that result from the properties of these two graphs are known as Nandu Sequences. 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 new public key cryptosystem introduced by Divesh Aggarwal et al.

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