Original Research Article

Article volume = 2024 and issue = 2

Pages: 181–192

Article publication Date: November 08, 2024

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Pair Mean Cordial Labeling of Total Graph of Some Graphs and Prism Related Graphs

R. Ponraj(a,∗), S. Prabhu(b), and M. Sivakumar(c)

(a) Department of Mathematics, Sri Paramakalyani College, Alwarkurichi–627 412, India, ORCID No.:0000-0001-7593-7429.

(b) Research Scholar, Reg.No:21121232091003, Department of Mathematics, Sri Paramakalyani College, Alwarkurichi–627 412,India (affiliated to Manonmaniam Sundaranar University, Tirunelveli-627 012, India) ORCID No.:0000-0003-3439-5330.

(c) Department of Mathematics, Government Arts and Science College, Tittagudi-606106, India, ORCID No.:0009-0006-2292-8258.

Abstract:

Let G = (V, E) be a graph with p vertices and q edges. Define ρ = { p/2 if p is even, (p−1)/2 if p is odd.}, and M = {±1,±2, · · ·±ρ}. Consider a mapping λ : V → M by assigning different labels in M to the different elements of V when p is even and different labels in M to p − 1 elements of V and repeating a label for the remaining one vertex when p is odd. The labeling as defined above is said to be a pair mean cordial labeling if for each edge uv of G, there is a labeling (λ(u)+λ(v))/2 if λ(u)+λ(v) is even and (λ(u)+λ(v)+1)/2 if λ(u) + λ(v) is odd such that |¯Sλ1 −¯Sλc1| ⩽ 1 where ¯Sλ1 and ¯Sλc1 respectively denote the number of edges labeled with 1 and the number of edges not labeled with 1. A graph G for which there is a pair mean cordial labeling is called a pair mean cordial graph (PMC-graph). In this paper, we investigate the pair mean cordial labeling behavior of some graphs like total graph of path, cycle, star, crown and comb and Also we examine the pair mean cordial labeling behavior of triangular winged prism graph, rectangular winged prism graph, W− graph and irregular pentagonal snake.

Keywords:

path, cycle, star, crown, comb, total graph.

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Cite this article as:
  • R. Ponraj, S. Prabhu, and M. Sivakumar, Pair Mean Cordial Labeling of Total Graph of Some Graphs and Prism Related Graphs, Communications in Combinatorics, Cryptography & Computer Science, 2024(2), PP.181–192, 2024
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