Structures of Digraphs Arizing from Lambert Type Maps

Authors

  • Tayyiba Sabahat Department of Mathematics, University of the Punjab, Lahore
  • Sufyan Asif Department of Mathematics, University of the Punjab, Lahore, Pakistan
  • Asif Abd ur Rehman Department of Mathematics, University of the Punjab, Lahore, Pakistan

DOI:

https://doi.org/10.21015/vtm.v9i1.1021

Abstract

The Well-known function W eW is called Lambert Map. This map has been viewed by many researchers for finding the approximate solutions of exponential function especially in numerical analysis. Later, it has been incorporated in number theory for finding integral solutions of exponential congruences under a fixed modulus. Instead of WeW, we use the function W2 e W and call this function as Discrete Lambert Type Function (DLTF). In this work, we produce graphs using DLTF, and discuss their structures. We show that the digraphs over DLTF satisfy many structures as these have been followed for using WeW.  It would be of great interest, if these results could be generalized for WeWfor all integers n, in the future.

References

Kannan, K., Narasimhan, D., Shanmugavelan, S. (2015). The Graph of Divisor Function D(n). International Journal of Pure and Applied Mathematics, 483-494.

Shanmugavelan, S. (2017). The Euler Function Graph G(ϕ(n)). International Journal of Pure and Applied Mathematics, 45-48.

Baskar Babujee, J. (2010). Euler’s Phi function and graph labelling. Int J. Contemp. Math. Sciences, 5(20), 977-984.

Madhavi, L., Maheswari, B. (2010). Enumeration of Hamilton cycles and Triangles in Euler Totient Cayley graphs. Graph Theory Notes of New York, LIX, 28-31.

Manjuri, M., Maheswari, B. (2013). Clique dominating sets of euler totient cayley graphs. IOSRJM, 4(6), 46-49.

Manjuri, M., Maheswari, B. (2012). Matching dominating sets of Euler-Totient-Cayley graphs. IJCER, 2(7), 103-107*.

Sangeetha, K. J., Maheswari, B. (2015). Edge domination in Euler-Totient-Cayley graph. IJSER, 3(2), 14-17*.

Niven, I., Zuckerman, H. S., Montgomery, H. L. (1991). An Introduction to the Theory of Numbers. John Wiley and Sons, Inc.

Malik, M. A., Mahmood, M. K. (2012). On simple graphs arising from exponential congruences. Journal of Applied Mathematics, Doi:10.1155/2012/292895.

Mahmood, M. K., Ahmad, F. (2015). A classification of cyclic nodes and enumerations of components of a class of discrete graphs. Appl. Math. Inf. Sci, 9(2015), 103-112*.

Mahmood, M. K., Ahmad, F. (2017). An informal enumeration of squares of 2 using rooted trees arising from congruences. Util. Math. 105(2017), 41-51*.

Mahmood, M. K., Ali, S. (2019). On super totient numbers with applications and algorithms to graph labelling. Ars Comb, 143(2019), 29-38*.

Mahmood, M. K., Anwar, L. (In Press). The Iteration Digraphs of Lambert Map Over the Local Ring mathbbZ/pkmathbbZ. Iranian Journal of Mathematical Sciences and Informatics.

Mahmood, M. K., Anwar, L. (2016). Loops in Digraphs of Lambert Mapping Modulo Prime Powers: Enumerations and Applications. Advances in Pure Mathematics, 8(2016), 564-570*.

Malik, M. A., Mahmood, M. K. (2012). On simple graphs arising from exponential congruences. Journal of Applied Mathematics, Doi:10.1155/2012/292895.

Mahmood, M. K., Ahmad, F. (2015). A classification of cyclic nodes and enumerations of components of a class of discrete graphs. Appl. Math. Inf. Sci, 9(2015), 103-112*.

Mahmood, M. K., Ahmad, F. (2017). An informal enumeration of squares of 2 using rooted trees arising from congruences. Util. Math. 105(2017), 41-51*

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Published

2021-12-31

How to Cite

Sabahat, T., Asif, S., & Rehman, A. A. ur. (2021). Structures of Digraphs Arizing from Lambert Type Maps. VFAST Transactions on Mathematics, 9(1), 28–36. https://doi.org/10.21015/vtm.v9i1.1021