Degree Sequence and Clique Number of
Bi-Factograph and Tri-Factograph

E. Ebin Raja Merly; E. Giftin Vedha Merly; A. M. Anto

doi:https://doi.org/10.14445/22315373/IJMTT-V21P506

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 21 | Number 1 | Year 2015 | Article Id. IJMTT-V21P506 | DOI : https://doi.org/10.14445/22315373/IJMTT-V21P506

Degree Sequence and Clique Number of Bi-Factograph and Tri-Factograph

E. Ebin Raja Merly, E. Giftin Vedha Merly, A. M. Anto

Citation :

E. Ebin Raja Merly, E. Giftin Vedha Merly, A. M. Anto, "Degree Sequence and Clique Number of Bi-Factograph and Tri-Factograph," International Journal of Mathematics Trends and Technology (IJMTT), vol. 21, no. 1, pp. 47-51, 2015. Crossref, https://doi.org/10.14445/22315373/IJMTT-V21P506

Abstract

By the theorem of unique factorization for integers, every positive integer 𝒛 can be written in the form 𝒛 = 𝒑𝟏 𝜶𝟏 𝒑𝟐 𝜶𝟐 …𝒑𝒓 𝜶𝒓 , where 𝒑𝟏,𝒑𝟐,… 𝒑𝒓 are distinct primes, 𝜶𝟏,𝜶𝟐,… 𝜶𝒓 are positive integers. We can construct a graph 𝑮 which is associated with this 𝒛. Positive integral divisors of 𝒛 being a vertex set 𝑽 and two distinct vertices of V are adjacent in 𝑮 if their product is in 𝑽. In z, when 𝒓 = 𝟏 then the corresponding graph is called the perfect factograph. Here we extend the concept to 𝒓 = 𝟐,𝟑 and the corresponding graphs are called Bi-factograph and Tri-factograph respectively. In this paper we attempt to find the degree sequence and clique number of Bi-factograph and Tri-factograph.

Keywords

Factograph, Perfect factograph, Bi-factograph, Tri-factograph, clique number.

References

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