### Structures of Digraphs Arizing from Lambert Type Maps

#### Abstract

The Well-known function W e^{W} 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 We^{W}, we use the function W^{2 }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 We^{W}. It would be of great interest, if these results could be generalized for We^{W}for all integers n, in the future.

#### Full Text:

PDF#### References

K. Kannan, D. Narasimhan, S. Shanmugavelan, THe Graph of Divisor Function

D(n), International Journal of Pure and Applied Mathematics, (2015)

-494

S. Shanmugavelan, The Euler FUnction Graph G(ϕ(n)), International Journal

of Pure and Applied Mathematics , (2017) 45-48

J. Baskar Babujee, Eyker’s Phi function and graph labelling, Int J. Contemp.

Math. Sciences, 5, No. 20, (2010), 977-984

L. Madhavi and B. Maheswari, Enumeration of Hamilton cycles and Triangles

in Euler Totient Cayley graphs, Graph Theory Notes of NewYork, LIX

(2010) 2831.

M. Manjuri, B. Maheswari, Clique dominating sets of euler totient cayley

graphs, IOSRJM, 4, No. 6 (2013), 46-49.

M. Manjuri, B. Maheswari, Matching dominating sets of Euler-TotientCayley

graphs, IJCER, 2, No. 7 (2012), 103-107.

K.J. Sangeetha, B. Maheswari, Edge domination in Euler-Totient-Cayley

graph, IJSER, 3, No. 2 (2015), 14-17.

I. Niven, H. S. Zuckerman, and H. L. Montgomery, An Introduction to the

Theory of Numbers, (John Wiley and Sons, Inc. 1991).

M.A Malik and M.K Mahmood, On simple graphs arising from exponential

congruences, Journal of Applied Mathematics Doi:10.1155/2012/292895.

M.K. Mahmood and F. Ahmad, A classiﬁcation of cyclic nodes and enumerations

of components of a class of discrete graphs, Appl. Math. Inf. Sci

(2015)103-112.

M.K. Mahmood and F. Ahmad, An informal enumeration of squares of 2

using rooted trees arising from congruences, Util. Math. 105(2017)41-51.

M. K. Mahmood, S. Ali, On super totient numbers with applications and

algorithms to graph labelling, Ars Comb 143(2019)29-38.

M. K. Mahmood, L. Anwar, The Iteration Digraphs of Lambert Map Over

the Local Ring mathbbZ/p

k

mathbbZ, Iranian Journal of Mathematical Sciences

and Informatics (In Press)

M. K. Mahmood, L. Anwar, Loops in Digraphs of Lambert Mapping Modulo

Prime Powers: Enumerations and Applications, Advances in Pure Mathematics

(2016)564-570.

M.A Malik and M.K Mahmood, On simple graphs arising from exponential

congruences, Journal of Applied Mathematics Doi:10.1155/2012/292895.

M.K. Mahmood and F. Ahmad, A classiﬁcation of cyclic nodes and enumerations

of components of a class of discrete graphs, Appl. Math. Inf. Sci

(2015)103-112.

M.K. Mahmood and F. Ahmad, An informal enumeration of squares of 2

using rooted trees arising from congruences, Util. Math. 105(2017)41-51.

k

k

DOI: http://dx.doi.org/10.21015/vtm.v9i1.1021

### Refbacks

- There are currently no refbacks.

This work is licensed under a Creative Commons Attribution 3.0 License.