A note on edge irregularity strength of firefly graph

Umme Salma, H. M. Nagesh and D. Prahlad
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 29, 2023, Number 1, Pages 147–153
DOI: 10.7546/nntdm.2023.29.1.147-153
Full paper (PDF, 1142 Kb)

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Authors and affiliations

Umme Salma
Department of Science & Humanities,
PES University, Bangalore, India

H. M. Nagesh
Department of Science & Humanities,
PES University, Bangalore, India

D. Prahlad
Department of Electronics and Communication Engineering,
PES University, Bangalore, India

Abstract

Let G be a simple graph. A vertex labeling \psi:V(G) \rightarrow \{1, 2,\ldots,\alpha\} is called \alpha-labeling. For an edge uv \in G, the weight of uv, written z_{\psi}(uv), is the sum of the labels of u and v, i.e., z_{\psi}(uv)=\psi(u)+\psi(v). A vertex \alpha-labeling is said to be an edge irregular \alpha-labeling of G if for every two distinct edges a and b, z_{\psi}(a) \neq z_{\psi}(b). The minimum \alpha for which the graph G contains an edge irregular \alpha-labeling is known as the edge irregularity strength of G and is denoted by \es(G). In this paper, we find the exact value of edge irregularity strength of different cases of firefly graph F_{s,t,n-2s-2t-1} for any s \geq 1, t \geq 1, n-2s-2t-1 \geq 1.

Keywords

  • Irregularity strength
  • Edge irregularity strength
  • Firefly graph

2020 Mathematics Subject Classification

  • 05C38
  • 05C78

References

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Manuscript history

  • Received: 13 September 2022
  • Revised: 15 February 2023
  • Accepted: 18 March 2023
  • Online First: 22 March 2023

Copyright information

Ⓒ 2023 by the Authors.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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Cite this paper

Salma, U., Nagesh, H. M., & Prahlad, D. (2023). A note on edge irregularity strength of firefly graph. Notes on Number Theory and Discrete Mathematics, 29(1), 147-153, DOI: 10.7546/nntdm.2023.29.1.147-153.

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