# Article ID: MTJPAM-D-21-00024

## Title: Power Exponential Mean Labeling of Graphs

Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-21-00024; Volume 3 / Issue 2 / Year 2021, Pages 70-79

Document Type: Research Paper

Author(s): Kurugal Munikempanna Nagaraja a , Sampathkumar Ramachandraiah b , Venkataramana Bathahalli Siddappa c

bDepartment of Mathematics, R N S Institute of Technology, Uttarahalli – Kengeri Main Road, R R Nagar post, Bengaluru, Karnataka, India

cDepartment of Mathematics, K S Institute of Technology, Kannakapura Main Road, Bengaluru, Karnataka, India

Received: 18 March 2021, Accepted: 14 May 2021, Published: 12 June 2021.

Corresponding Author: Kurugal Munikempanna Nagaraja (Email address: nagkmn@gmail.com)

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Abstract

A  $(p, q)$  graph  $G$  is said to be a power exponential mean graph if there exist a one to one correspondence  $f:V\rightarrow\{1,2,3,\ldots,p\}$  such that induced function  $f^*:E(G)\rightarrow N$  given by

$f^* (uv)=\left\lceil{\left({f(u) }^{f(u)}{f(v)}^{f(v)}\right)}^{\frac{1}{f(u)+f(v)}}\right\rceil \qquad \text{or} \qquad f^* (uv)=\left\lfloor{\left({f(u) }^{f(u)}{f(v)}^{f(v)}\right)}^{\frac{1}{f(u)+f(v)}}\right\rfloor$

for every  $uv\in E(G)$  are all distinct. In this paper the power exponential mean labeling of graphs such as path, cycle,  $K_1+C_n$  for  $n$  is odd and even, square graph, umbrella  $U(m,n)$, duplicating each vertex by an edge in path  $P_n$, comb,  $C_m\bigodot \overline{ K_1}$  and  $C_n\bigodot \overline{ K_2}$  are discussed.

Keywords: Graph, power exponential mean, path, cycle, square graph, umbrella, comb

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