Graceful Labeling of Prime Index Graph of Group Zp × Zpn

Authors

  • Renu Department of Mathematics, Maharshi Dayanand University, Rohtak (Haryana), India
  • Sarita Department of Mathematics, Govt. (PG) College for Women, Rohtak (Haryana), India
  • Amit Sehgal Department of Mathematics, Pt. NRS Govt. College, Rohtak (Haryana), India https://orcid.org/0000-0001-7820-8037
  • Archana Malik Department of Mathematics, Maharshi Dayanand University, Rohtak (Haryana), India

DOI:

https://doi.org/10.37256/cm.4320232727

Keywords:

ladder graph, path graph, prime index graph, graceful graph and graceful labeling

Abstract

The prime index graph π(G) of a finite group G is a special type of undirected simple graph whose vertex set is set of subgroups of G, in which two distinct vertices are adjacent if one has prime index in the other. Let p and q be distinct primes. In this paper, we establish that prime index graph of a finite cyclic p-group Zpn, a finite abelian group Zpn × Zq and a finite abelian p-group Zp × Zpn always have graceful labeling without any condition on n using the concept of path graph or p-layer ladder graph of size n + 1.

Downloads

Published

2023-09-18

How to Cite

1.
Renu, Sarita, Sehgal A, Archana Malik. Graceful Labeling of Prime Index Graph of Group Zp × Zpn. Contemp. Math. [Internet]. 2023 Sep. 18 [cited 2024 Mar. 4];4(3):612–619. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/2727