H. M. Nagesh and V. R. Girish

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 28, 2022, Number 3, Pages 517–524

DOI: 10.7546/nntdm.2022.28.3.517-524

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## Details

### Authors and affiliations

H. M. Nagesh

*Department of Science & Humanities, PES University
Electronic City Campus, Hosur Road, Bangalore – 560 100, India
*

V. R. Girish

*Department of Science & Humanities, PES University
Electronic City Campus, Hosur Road, Bangalore – 560 100, India
*

### Abstract

For a simple graph , a vertex labeling is called -labeling. The weight of an edge in , written , is the sum of the labels of end vertices and , i.e., . A vertex -labeling is defined to be an edge irregular -labeling of the graph if for every two different edges and , . The minimum for which the graph has an edge irregular -labeling is called the edge irregularity strength of , written . In this paper, we find the exact value of edge irregularity strength of line graph of comb graph for ; and determine the bounds for . Also, the edge irregularity strength of line cut-vertex graph of for ; and determine the bounds for .

### Keywords

- Irregular assignment
- Irregularity strength
- Irregular total -labeling
- Edge irregularity strength
- Comb graph

### 2020 Mathematics Subject Classification

- 05C38
- 05C78

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### Manuscript history

- Received: 4 March 2022
- Revised: 2 August 2022
- Accepted: 4 August 2022
- Online First: 10 August 2022

## Related papers

## Cite this paper

Nagesh, H. M, & Girish, V. R. (2022). On edge irregularity strength of line graph and line cut-vertex graph of comb graph. *Notes on Number Theory and Discrete Mathematics*, 28(3), 517-524, DOI: 10.7546/nntdm.2022.28.3.517-524.