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

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

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

2022
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Overview
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.