Supersubdivision in the Context of AUM Block Labeling for Coconut Tree and Double Coconut Tree Graph

Authors

  • J. Jeba Jesintha PG Department of Mathematics, Women’s Christian College (University of Madras), Chennai 600006, Tamil Nadu, India https://orcid.org/0000-0002-4568-4499
  • D. Devakirubanithi Department of Mathematics, St. Thomas College of Arts and Science (University of Madras), Chennai 600107, Tamil Nadu, India https://orcid.org/0000-0002-9566-543X
  • H. Christa Miracline PG Department of Mathematics, Women’s Christian College (University of Madras), Chennai 600006, Tamil Nadu, India

DOI:

https://doi.org/10.26713/jims.v17i2.3146

Abstract

A graph \(G\) with \(p\) number of vertices, \(q\) number of edges and \(b\) number of blocks, where \(p,q,b\ge 1\). The set of vertices, edges and blocks are denoted by \(V(G)=\{v_1,v_2,\dots ,v_p\}\), \(E(G)=\{e_1,e_2,\dots ,e_q\}\) and \(B(G)=\{b_1,b_2,\dots ,b_n\}\), respectively. The graph \(G\) admits AUM block labeling if there exists a bijection \(f:V(G)\rightarrow z^+\) induced from \(f\) by \(f^*(uv)=f(u)*f(v)\) and \(f^{**}(B_j)=B(G)\rightarrow z^+\) then \(f^{**}(B_j)=\sum^n_{i=1}{f}(v_{ij})+\sum^n_{i=1}f^*(e_{ij})\) and \(f^{**}(B_i)\neq f^{**}(B_j)\). In this paper, we prove that the super subdivision of coconut tree and double coconut tree graph admits AUM block labeling.

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Published

2025-06-30
CITATION

How to Cite

Jesintha, J. J., Devakirubanithi, D., & Christa Miracline, H. (2025). Supersubdivision in the Context of AUM Block Labeling for Coconut Tree and Double Coconut Tree Graph. Journal of Informatics and Mathematical Sciences, 17(2), 187–192. https://doi.org/10.26713/jims.v17i2.3146

Issue

Vol. 17 No. 2 (2025)

Section

Research Article

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